API

ModelGeometry{T, B<:AbstractVector{<:AbstractVector{T}}}

A type defining the geometry of a lattice model, including the unit cell, lattice, and bond definitions.

• unit_cell::UnitCell: contains unit cell definitions.
• lattice::Lattice: contains lattice definitions including boundary conditions.
• bond::B: vector of all bond definitions.

apply_twist_angle!( H_t::Matrix{T},
                    θ_twist::E,
                    model_geometry::ModelGeometry ) where {T<:Number, E<:AbstractFloat}

Applies a twist angle to the hopping matrix by multiplying by an appropriate phase factor.

x( i::I, 
   model_geometry::ModelGeometry ) where {I<:Integer}

Convenience function for obtaining the x-coordinate of a lattice site given a lattice spindex.

• i::I: spindex.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

y( i::I, 
   model_geometry::ModelGeometry ) where {I<:Integer}

Convenience function for obtaining the y-coordinate of a lattice site given a lattice spindex.

• i::I: spindex.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

d( p1::I, 
   p2::I, 
   model_geometry::ModelGeometry ) where {I<:Integer}

Given lattice points $p\_1$ and $p_2$, returns the distance between those two points, accounting for the lattice edges under different boundary conditions.

• p1::I: first lattice point.
• p2::I: second lattice point.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

reduce_index_2d( i::I, 
                 j::I, 
                 model_geometry::ModelGeometry ) where {I<:Integer}

For two lattice sites $i$ and $j$ on a 2D lattice, returns the irreducible index $k$ between them, where $k$ is an integer.

• i::I: first lattice site.
• j::I: second lattice site.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

reduce_index_1d( i::I, 
                 j::I, 
                 model_geometry::ModelGeometry ) where {I<:Integer}

For two lattice sites $i$ and $j$ on a 1D lattice, returns the irreducible index $k$ between them, where $k$ is an integer.

• i::I: first lattice site.
• j::I: second lattice site.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

max_dist( N::I, 
          L::I ) where {I<:Integer}

For a lattice with $N$ sites and extent $L$, returns the maximum irreducible index $k_{\mathrm{max}}$.

• N::I: total number of lattice sites.
• L::I: extent of the lattice.

TightBindingModel{E<:AbstractFloat}

A type defining a non-interacting tight binding model with nearest, next nearest, and third nearest hopping parameters.

• t₀::E: zeroth hopping parameter (nearest neighbor)
• t₁::E: first hopping parameter (next nearest neighbor)
• t₂::E: second hopping parameter (third nearest neighbor)

SpinModel{E<:AbstractFloat}

A type defining a non-interacting spin model with nearest, next nearest, and third nearest neighbor exchange coupling parameters.

DeterminantalParameters{I<:Integer}

A type defining a set of variational parameters obtained from the auxiliary Hamiltonian, otherwise known as the "determinantal" part of the variational wavefunction.

• det_pars::NamedTuple: contains parameter names and their values.
• num_det_pars::I: total number of determinantal parameters.
• num_det_opts::I: number of determinantal parameters being optimized.

JastrowParameters{S<:AbstractString, K, V, I<:Integer}

A type defining quantities related to Jastrow variational parameters.

• jastrow_type::S: type of Jastrow parameters: "e-den-den", "e-spn-spn"
• jpar_map::OrderedDict{K, V}: dictionary of irreducible indices to their correct index pairs and Jastrow parameter.
• num_jpars::I: total number of Jastrow parameters.
• num_jpar_opts::I: total number of Jastrow parameters being optimized.

collect_parameters( determinantal_parameters::DeterminantalParameters{I}, 
                    jastrow_parameters::JastrowParameters{S, K, V, I} ) where {S<:AbstractString, K, V, I<:Integer}

Concatenates all values of determinantal and Jastrow parameters into a single vector of variational parameters.

• determinantal_parameters::DeterminantalParameters{I}: current set of determinantal parameters.
• jastrow_parameters::JastrowParameters{S, K, V, I}: current set of Jastrow parameters.

collect_parameters( determinantal_parameters::DeterminantalParameters{I}, 
                    jastrow_parameters_1::JastrowParameters{S, K, V, I},
                    jastrow_parameters_2::JastrowParameters{S, K, V, I} ) where {S<:AbstractString, K, V, I<:Integer}

Concatenates all values of determinantal and Jastrow parameters into a single vector of variational parameters.

• determinantal_parameters::DeterminantalParameters{I}: current set of determinantal parameters.
• jastrow_parameters_1::JastrowParameters{S, I, V}: first set of Jastrow parameters.
• jastrow_parameters_2::JastrowParameters{S, I, V}: second set of Jastrow parameters.

update_parameters!( measurement_container::NamedTuple,
                    new_vpars::AbstractVector, 
                    determinantal_parameters::DeterminantalParameters{I} ) where {I<:Integer}

Updates variational parameters after Stochastic Reconfiguration.

• measurement_container::NamedTuple: container where measurements are stored.
• new_vpars::AbstractVector: updated variational parameters.
• determinantal_parameters::DeterminantalParameters{I}: current set of determinantal variational parameters.

update_parameters!( measurement_container::NamedTuple,
                    new_vpars::AbstractVector, 
                    determinantal_parameters::DeterminantalParameters{I}, 
                    jastrow_parameters::JastrowParameters{S, K, V, I} ) where {S<:AbstractString, K, V, I<:Integer}

Updates variational parameters after Stochastic Reconfiguration.

• measurement_container::NamedTuple: container where measurements are stored.
• new_vpars::AbstractVector: updated variational parameters.
• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• jastrow_parameters::JastrowParameters{S, K, V, I}: set of Jastrow variational parameters.

update_parameters!( measurement_container::NamedTuple,
                    new_vpars::AbstractVector, 
                    determinantal_parameters::DeterminantalParameters{I}, 
                    jastrow_parameters_1::JastrowParameters{S, K, V, I},
                    jastrow_parameters_2::JastrowParameters{S, K, V, I} ) where {S<:AbstractString, K, V, I<:Integer}

Updates variational parameters after Stochastic Reconfiguration.

• measurement_container::NamedTuple: container where measurements are stored.
• new_vpars::AbstractVector: updated variational parameters.
• determinantal_parameters::DeterminantalParameters{I}: current set of determinantal variational parameters.
• jastrow_parameters::JastrowParameters{S, K, V, I}: first set of Jastrow variational parameters.
• jastrow_parameters::JastrowParameters{S, K, V, I}: second set of Jastrow variational parameters.

readin_parameters( filename::S ) where {S<:AbstractString}

Parses TOML file containing initial variational parameters.

• filename::S: name of parameter summary file in TOML format.

build_auxiliary_hamiltonian( tight_binding_model::TightBindingModel{E}, 
                             determinantal_parameters::DeterminantalParameters{I}, 
                             optimize::NamedTuple, 
                             model_geometry::ModelGeometry, 
                             pht::Bool;
                             q_p::AbstractVector{T} = [0.0, 0.0] ) where {E<:AbstractFloat, I<:Integer}

Constructs an auxiliary Hamiltonian matrix $H_{\mathrm{aux}}$ by combining the non-interacting hopping matrix $H_t$ with matrices of variational terms $H_{\mathrm{var}}$.

• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• optimize::NamedTuple: field of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hol transformed.
• q_p::AbstractVector{T} = [0.0, 0.0]: pairing momentum for density wave pairing.

build_auxiliary_hamiltonian( tight_binding_model::TightBindingModel{E}, 
                             determinantal_parameters::DeterminantalParameters{I}, 
                             optimize::NamedTuple, 
                             model_geometry::ModelGeometry, 
                             twist_angles::AbstractRange{E},
                             pht::Bool;
                             q_p::AbstractVector{T} = [0.0, 0.0] ) where {E<:AbstractFloat, I<:Integer}

Constructs an auxiliary Hamiltonian matrix $H_{\mathrm{aux}}^{\theta}$ for $N_\theta$ twist angles by combining the non-interacting hopping matrix $H_t$ with matrices of variational terms $H_{\mathrm{var}}$.

• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• optimize::NamedTuple: field of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• twist_angles::AbstractRange{E}: set of twist angles.
• pht::Bool: whether model is particle-hol transformed.
• q_p::AbstractVector{T} = [0.0, 0.0]: pairing momentum for density wave pairing.

build_tight_binding_hamiltonian( tight_binding_model::TightBindingModel{E},
                                 model_geometry::ModelGeometry,
                                 pht::Bool ) where {E<:AbstractFloat}

Constructs a $2N$ by $2N$ tight-binding hopping matrix where $N$ is the number of lattice sites, given hopping parameters $t$, $t^{\prime}$, and $t^{\prime\prime}$.

• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

build_variational_hamiltonian( determinantal_parameters::DeterminantalParameters{I}, 
                               model_geometry::ModelGeometry,
                               optimize::NamedTuple, 
                               pht::Bool;
                               q_p::AbstractVector{T} = [0.0, 0.0] ) where {I<:Integer}

Constructs a set of $2N$ by $2N$ matrices for each variational parameter, where N is the number of lattice sites. Returns a total variational Hamiltonian matrix $H_{\mathrm{var}}$ as well has a vector of operators $V$.

• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• optimize::NamedTuple: field of optimization flags.
• pht::Bool: whether model is particle-hole transformed.
• q_p::AbstractVector{T} = [0.0, 0.0]: pairing momentum for density wave pairing.

add_pairing_symmetry!( symmetry::S, 
                       optimize::NamedTuple, 
                       H_vpars::Vector{Matrix{T}}, 
                       V::Vector{Matrix{T}}, 
                       model_geometry::ModelGeometry,
                       bonds,
                       dims::I,
                       N::I, 
                       pht::Bool;
                       q_p::AbstractVector{T} = [0.0, 0.0],
                       locs::Vector{Tuple{I, I}} = Tuple{I,I}[] ) where {S<:AbstractString, I<:Integer, T<:Number}

Adds a pairing term to the auxiliary Hamiltonian along with its perturbative operator.

• symmetry::S: type of pairing symmetry: "s", "d", "sLO", "sFF", "dLO", or "dFF".
• optimize::NamedTuple: field of optimization flags.
• H_vpars::Vector{Matrix{T}}: vector of variational Hamiltonian matrices.
• V::Vector{Matrix{T}}: vector of variational operators.
• model_geometry::ModelGeometry: contains lattice and unit cell quantities.
• dims::I: dimensions of the lattice.
• bonds: lattice bonds.
• N::I: number of sites in the lattice.
• pht::Bool: whether model is particle-hole transformed.
• q_p::AbstractVector{T} = [0.0, 0.0]: pairing momentum for density wave pairing.
• locs::Vector{Tuple{I, I}} = Tuple{I,I}[]: contains all positions (or locations) of each lattice site.

add_spin_order!( order::S, 
                 optimize::NamedTuple, 
                 H_vpars::Vector{Matrix{T}}, 
                 V::Vector{Matrix{T}}, 
                 model_geometry::ModelGeometry,
                 locs::,
                 dims::I,
                 N::I, 
                 pht::Bool )::Nothing

Adds a spin ordering term to the auxiliary Hamiltonian along with its perturbative operator.

• order::String: type of spin order: "spin-x", "spin-z", or "site-dependent"
• optimize::NamedTuple: field of optimization flags.
• H_vpars::Vector{Any}: vector of variational Hamiltonian matrices.
• V::Vector{Any}: vector of variational operators.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• locs::: preallocated
• dims::I: dimensions of the lattice.
• N::I: number of sites in the lattice.
• pht::Bool: whether model if particle-hole transformed.

add_charge_order!( order::S, 
                   optimize::NamedTuple, 
                   H_vpars::Vector{Matrix{T}}, 
                   V::Vector{Matrix{T}}, 
                   model_geometry::ModelGeometry,
                   locs::,
                   dims::I,
                   N::I, 
                   pht::Bool ) where {S<:AbstractString, I<:Integer, T<:Number}

Adds a charge ordering term to the auxiliary Hamiltonian along with its perturbative operator.

• order::S: type of spin order: "density wave" or "site-dependent"
• optimize::NamedTuple: field of optimization flags.
• H_vpars::Vector{Matrix{T}}: vector of variational Hamiltonian matrices.
• V::Vector{Matrix{T}}: vector of variational operators.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• locs:::
• dims::I: dimensions of the lattice.
• N::I: number of sites in the lattice.
• pht::Bool: whether model if particle-hole transformed.

add_chemical_potential!( optimize::NamedTuple, 
                         H_vpars::Vector{Matrix{T}}, 
                         V::Vector{Matrix{T}}, 
                         N::I, 
                         pht::Bool ) where {T<:Number, I<:Integer}

Adds a chemical potential term to the auxiliary Hamiltonian.

• optimize::NamedTuple: field of optimization flags.
• H_vpars::Vector{Matrix{T}}: vector of variational Hamiltonian matrices.
• V::Vector{Matrix{T}}: vector of variational operators.
• N::I: number of sites in the lattice.
• pht::Bool: whether model if particle-hole transformed.

diagonalize!( H::Matrix{T} ) where {T<:Number}

Returns all eigenenergies $\varepsilon$ and all eigenstates $\phi$ of the auxiliary Hamiltonian matrix. All eigenstates are stored in the columns of a unitary matrix U_aux.

• H::Matrix{T}: auxiliary Hamiltonian matrix.

is_openshell( ε::Vector{E},  
              Np::I,
              pht::Bool ) where {E<:AbstractFloat, I<:Integer}

Checks whether a mean-field energy configuration is open shell.

• ε::Vector{E}: vector of mean-field energies.
• Np::I: total number of particles in the system.
• pht::Bool: whether the model is particle-hole transformed.

get_variational_matrices( V::Vector{Matrix{T1}}, 
                          U_aux::Matrix{T2}, 
                          ε::Vector{E}, 
                          Np::I
                          N::I ) where {T1<:Number, T2<:Number, E<:AbstractFloat, I<:Integer}

Returns a set of variational parameter matrices $A_k$ constructed from each variational operator $V_k$ by computing

\[Q_k = \frac{(U^{\dagger}V_{k}U)_{\eta\nu}}{(\varepsilon_{\eta} - \varepsilon_{\nu})},\]

where $\eta > N_p$ and $\nu \leq N_p$.

• V::Vector{Matrix{T1}: vector of variational operators.
• U_aux::Matrix{T2}: matrix which diagonalizes the auxiliary Hamiltonian.
• ε::Vector{E}: initial energies.
• Np::I: number of particles in the system.
• N::I: number of lattice sites.

get_tb_chem_pot( Ne::I, 
                 tight_binding_model::TightBindingModel{E}, 
                 model_geometry::ModelGeometry ) where {I<:Integer, E<:AbstractFloat}

Computes the appropriate chemical potential $\mu$ for a non-interacting tight-binding model on a finite lattice.

• Ne::I: total number of electrons.
• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

DeterminantalWavefunction{T<:Number, Q, E<:AbstractFloat, I<:Integer}

A type defining quantities related to a determinantal wavefunction.

• W::Matrix{T}: equal-time Green's function matrix.
• D::Matrix{T}: Slater matrix.
• M::AbstractMatrix{T}: reduced U_aux matrix.
• U_aux::Matrix{T}: unitary matrix that diagonalizes the auxiliary Hamiltonian.
• A::Vector{Q}: variational parameter matrices.
• ε::Vector{E}: vector of mean-field energies.
• pconfig::Vector{I}: particle configuration.
• nq_updates_W::I: tracker for the number for quick updates to the W matrix.

DeterminantalWavefunctionTABC{T<:Number, Q, E<:AbstractFloat, I<:Integer}

A type defining quantities related to a determinantal wavefunction over a range of twist angles.

• W_θ::Vector{Matrix{T}}: set of equal-time Green's function matrices.
• D_θ::Vector{Matrix{T}}: set of Slater matrices.
• M_θ::Vector{AbstractMatrix{T}}: set of reduced U_aux matrices.
• U_θ::Vector{Matrix{T}}: set of unitary matrices that diagonalizes the auxiliary Hamiltonian.
• A_θ::Vector{Vector{Q}}: set of variational parameter matrices.
• ε_θ::Vector{Vector{E}}: vector of mean-field energies.
• pconfig::Vector{I}: particle configuration.
• N_θ::I: number of twist angles to average over.
• twist_angles::AbstractRange{E}: set of twist angles.
• nq_updates_W::I: tracker for the number for quick updates to the W matrix.

get_determinantal_wavefunction( tight_binding_model::TightBindingModel{E}, 
                                determinantal_parameters::DeterminantalParameters{I}, 
                                optimize::NamedTuple, 
                                Np::I, 
                                nup::I, 
                                ndn::I, 
                                model_geometry::ModelGeometry, 
                                rng::AbstractRNG, 
                                pht::Bool,
                                pconfig::Vector{I} = Int[];
                                q_p::AbstractVector{T} = [0.0, 0.0] ) where {E<:AbstractFloat, I<:Integer, T<:Number}

Constructs a variational wavefunction $|\Phi_0\rangle$ based on parameters given by the tight-binding model and determinantal parameter and returns an instance of the DeterminantalWavefunction type. If no initial particle configuration is specified, a random configuration will be generated.

• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• optimize::NamedTuple: field of optimization flags.
• Np::I: total number of particles in the system.
• nup::I: number of spin-up electrons.
• ndn::I: number of spin-down electrons.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• rng::AbstractRNG: random number generator.
• pht::Bool: whether model is particle-hole transformed.
• pconfig::Vector{I} = Int[]: optional initial particle configuration.
• q_p::AbstractVector{T} = [0.0, 0.0]: pairing momentum for density wave pairing.

get_determinantal_wavefunction( tight_binding_model::TightBindingModel{E}, 
                                determinantal_parameters::DeterminantalParameters{I}, 
                                optimize::NamedTuple, 
                                Np::I, 
                                nup::I, 
                                ndn::I, 
                                model_geometry::ModelGeometry, 
                                N_θ::I,
                                twist_angles::AbstractRange{E},
                                rng::AbstractRNG, 
                                pht::Bool,
                                pconfig::Vector{I} = Int[] ) where {E<:AbstractFloat, I<:Integer}

Constructs a variational wavefunction $|\Phi_{0}^{\theta}\rangle$ for N_\theta twist angles based on parameters given by the tight-binding model and determinantal parameter and returns an instance of the DeterminantalWavefunctionTABC type. If no initial particle configuration is specified, a random configuration will be generated.

• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• optimize::NamedTuple: field of optimization flags.
• Np::I: total number of particles in the system.
• nup::I: number of spin-up electrons.
• ndn::I: number of spin-down electrons.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• N_θ::I: number of twist angles.
• twist_angles::AbstractRange{E}: list of twist angles.
• rng::AbstractRNG: random number.
• pht::Bool: whether model is particle-hole transformed.
• pconfig::Vector{I} = Int[]: optional initial particle configuration.

JastrowFactor{E<:AbstractFloat, I<:Integer}

A type defining quantities related to a Jastrow factor.

• Tvec_f::Vector{E}: fermionic T vector.
• Tvec_b::Vector{E}: bosonic or phononic T vector.
• nq_updates_T::I: tracker for the number of quick updates to the T vector.

get_jastrow_factor( jastrow_parameters::JastrowParameters{S, K, V, I}, 
                    detwf::DeterminantalWavefunction{T, Q, E, I}, 
                    model_geometry::ModelGeometry, 
                    pht::Bool )::JastrowFactor

Given a set of Jastrow parameters, constructs the relevant Jastrow factor $\mathcal{J}_n$ and returns a instance of the JastrowFactor type.

• jastrow_parameters::JastrowParameters{S, K, V, I}: current set of Jastrow parameters.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

get_fermionic_Tvec( jastrow_type::S,  
                    jpar_map::OrderedDict{Any, Any},
                    detwf::DeterminantalWavefunction{T, Q, E, I}, 
                    N::I,
                    pht::Bool )

Returns a fermionic T vector with elements $T_{i} = \sum_{j} v_{ij} n_{i}$ where $v\_{ij}$ are the Jastrow peseudopotentials and $n_{i}$ are the total fermion occupations.

• jastrow_type::S: either "e-den-den" or "e-spn-spn.
• jpar_map::OrderedDict{Any, Any}: current map of Jastrow parameters.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• N::I: number of lattice sites.
• pht::Bool: whether model is particle-hole transformed.

update_fermionic_Tvec!( markov_move::MarkovMove{I}, 
                        spin::I, 
                        jastrow_parameters::JastrowParameters{S, K, V, I},
                        jastrow_factor::JastrowFactor{E}, 
                        detwf::DeterminantalWavefunction,
                        model_geometry::ModelGeometry, 
                        n_stab_T::I, 
                        δT::E, 
                        pht::Bool ) where {S<:AbstractString, K, V, I<:Integer, E<:AbstractFloat}

Updates elements $T_{i}$ of the fermion-type T vector after an accepted Metropolis step.

• markov_move::MarkovMove{I}: quantities related to a Markov process.
• spin::I: spin of the current particle.
• jastrow_parameters::JastrowParameters{S, K, V, I}: current set of Jastrow variational parameters.
• jastrow::JastrowFactor{E}: current Jastrow factor.
• detwf::DeterminantalWavefunction: current determinantal wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• n_stab_T::I: frequency of T vector stabilization setps.
• δT::E: deviation threshold for the T vector.
• pht::Bool: whether model is particle-hole transformed.

get_fermionic_jastrow_ratio( markov_move::MarkovMove{I}, 
                             jastrow_parameters::JastrowParameters{S, K, V, I},
                             jastrow_factor::JastrowFactor{E}, 
                             pht::Bool, 
                             spin::I, 
                             model_geometry::ModelGeometry ) where {I<:Integer, S<:AbstractString, K, V, E<:AbstractFloat}

Calculates ratio of fermionic Jastrow factors

\[\frac{\mathcal{J}_1}{\mathcal{J}_2} = \exp[s(T_{l} - T_{k}) + v_{ll} - v_{lk}],\]

after a single particle completes a move from site $k$ to site $l$ using the corresponding T vectors $T_k$ and $T_l$.

• markov_move::MarkovMove{I}: quantities related to a Markov process.
• jastrow_parameters::JastrowParameters{S, K, V, I}: current set of Jastrow variational parameters.
• jastrow_factor::JastrowFactor{E}: current Jastrow factor.
• pht::Bool: whether model is particle-hole transformed.
• spin::I: spin of the current particle.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

get_fermionic_jastrow_ratio( k::I, 
                             l::I, 
                             jastrow_parameters::JastrowParameters{S, K, V, I},
                             jastrow_factor::JastrowFactor{E}, 
                             pht::Bool, 
                             spin::I, 
                             model_geometry::ModelGeometry ) where {I<:Integer, S<:AbstractString, K, V, E<:AbstractFloat}

Calculates ratio of fermionic Jastrow factors

\[\frac{\mathcal{J}_1}{\mathcal{J}_2} = \exp[-s(T_{l} - T_{k}) + v_{ll} - v_{lk}],\]

after a single particle completes a move from site $k$ to site $l$ using the corresponding T vectors $T_k$ and $T_l$.

• k::Int: initial site of the current particle.
• l::Int: final site of the current particle.
• jastrow_parameters::JastrowParameters: current set of Jastrow variational parameters.
• jastrow_factor::JastrowFactor: current Jastrow factor.
• pht::Bool: whether model is particle-hole transformed.
• spin::Int: spin of the current particle.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

map_jastrow_parameters( model_geometry::ModelGeometry, 
                        rng::AbstractRNG )

Generates a dictionary of irreducible index keys $k$ with values being a tuple of all lattice index pairs $(i,j)$, which generate $k$, and their associated Jastrow parameter $v_{ij}$. The parameter corresponding to the largest irreducible index is initialized to zero.

• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• rng::AbstractRNG: random number generator.

map_jastrow_parameters( model_geometry::ModelGeometry, 
                        init_jpars::Vector{E} ) where {E<:AbstractFloat}

Given an initial set of Jastrow parameters from file, generates a dictionary of irreducible index keys $k$ with values being a tuple of all lattice index pairs $(i,j)$, which generate $k$, and their associated Jastrow parameter $v_{ij}$. The parameter corresponding to the largest irreducible index is initialized to zero.

• model_geometry::ModelGeometry: contains unit cell and lattice qunatities.
• init_jpars::Vector{E}: initial Jastrow parameters from file.

local_fermion_update!( detwf::DeterminantalWavefunction{T, V, E, I},
                       Np::I, 
                       model_geometry::ModelGeometry, 
                       n_stab_W::I,
                       δW::E, 
                       rng::AbstractRNG ) where {T<:Number, V, E<:AbstractFloat, I<:Integer}

Performs a local update to the fermionic sector by attempting to move a particle $\beta$ at a randomly selected lattice site $k$ to another random site $l$, with the move accepted or rejected by the Meteropolis algorithm.

• detwf::DeterminantalWavefunction{T, V, E, I}: current determinantal variational wavefunction.
• Np::I: total number of particles in the system.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• n_stab_W::I: frequency of Green's function stabilization steps.
• δW::E: error threshold for the Green's function.
• rng::AbstractRNG: random number generator.

local_fermion_update!( detwf::DeterminantalWavefunction{T, Q, E, I}, 
                       jastrow_factor::JastrowFactor{E}, 
                       jastrow_parameters::JastrowParameters{S, K, V, I},
                       Np::I, 
                       model_geometry::ModelGeometry, 
                       pht::Bool, 
                       n_stab_W::I,
                       n_stab_T::Int,
                       δW::E, 
                       δT::E, 
                       rng::AbstractRNG ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, K, V}

Performs a local update to the fermionic sector by attempting to move a particle $\beta$ at a randomly selected lattice site $k$ to another random site $l$, with the move accepted or rejected by the Meteropolis algorithm.

• detwf::DeterminantalWavefunction{T, Q, E, I}: current determinantal variational wavefunction.
• jastrow_facor::JastrowFactor{E}: current Jastrow factor.
• jastrow_parameters::JastrowParameters{S, K, V, I}: current set of Jastrow variational parameters.
• Np::I: total number of particles in the system.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.
• n_stab_W::I: frequency of Green's function stabilization steps.
• n_stab_T::I: frequency of T vector stabilization steps.
• δW::E: error threshold for the Green's function.
• δT::E: error treshold for the Jastrow T vector.
• rng::AbstractRNG: random number generator.

local_fermion_update!( detwf::DeterminantalWavefunction{T, Q, E, I}, 
                       jastrow_factor_1::JastrowFactor{E}, 
                       jastrow_factor_2::JastrowFactor{E}, 
                       jastrow_parameters_1::JastrowParameters{S, K, V, I},
                       jastrow_parameters_2::JastrowParameters{S, K, V, I},
                       Np::I, 
                       model_geometry::ModelGeometry, 
                       pht::Bool, 
                       n_stab_W::I,
                       n_stab_T::I,
                       δW::E, 
                       δT::E, 
                       rng::Xoshiro ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, K, V}

Performs a local update to the fermionic sector by attempting to move a particle $\beta$ at a randomly selected lattice site $k$ to another random site $l$, with the move accepted or rejected by the Meteropolis algorithm.

• detwf::DeterminantalWavefunction{T, Q, E, I}: current determinantal variational wavefunction.
• jastrow_factor_1::Jastrow{E}: first Jastrow factor.
• jastrow_factor_2::Jastrow{E}: second Jastrow factor.
• jastrow_parameters_1::JastrowParameters{S, K, V, I}: first set of Jastrow variational parameters.
• jastrow_parameters_2::JastrowParameters{S, K, V, I}: second set of Jastrow variational parameters.
• Np::I: total number of particles in the system.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• n_stab_W::I: frequency of Green's function stabilization steps.
• n_stab_T::I: frequency of T vector stabilization steps.
• δW::E: error threshold for the Green's function.
• δT::E: error treshold for the Jastrow T vector.
• rng::AbstractRNG: random number generator.

metropolis_step( detwf::DeterminantalWavefunction{T, Q, E, I}, 
                 Np::I, 
                 n_stab_W::I, 
                 δW::E,
                 model_geometry::ModelGeometry, 
                 rng::AbstractRNG ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Attempts to move particle $\beta$ at lattice site $k$ to a randomly selected site $l$.

• detwf::DeterminantalWavefunction{T, Q, E, I}: current determinantal variational wavefunction.
• Np::I: total number of particles in the system.
• n_stab_W::I: frequency of Green's function stabilization steps.
• δW::E: error threshold for the Green's function.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• rng::AbstractRNG: random number generator.

metropolis_step( detwf::DeterminantalWavefunction{T, Q, E, I}, 
                 jastrow_factor::JastrowFactor{E}, 
                 jastrow_parameters::JastrowParameters{S, K, V, I},
                 Np::I, 
                 n_stab_W::I, 
                 n_stab_T::I, 
                 δW::E, 
                 δT::E, 
                 model_geometry::ModelGeometry, 
                 pht::Bool, 
                 rng::AbstractRNG ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Attempts to move particle $\beta$ at lattice site $k$ to a randomly selected site $l$.

• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• jastrow_factor::JastrowFactor{E}: current Jastrow factor.
• jastrow_parameters::JastrowParameters{S, K, V, I}: current set of Jastrow parameters.
• Np::I: total number of particles in the system.
• n_stab_W::I: frequency of Green's function stabilization steps.
• n_stab_T::I: frequency of T vector stabilization steps.
• δW::E: error threshold for the Green's function.
• δT::E: error threshold for the T vector.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.
• rng::AbstractRNG: random number generator.

metropolis_step( detwf::DeterminantalWavefunction{T, Q, E, I}, 
                 jastrow_factor_1::JastrowFactor{E}, 
                 jastrow_factor_2::JastrowFactor{E},
                 jastrow_parameters_1::JastrowParameters{S, K, V, I}, 
                 jastrow_parameters_2::JastrowParameters{S, K, V, I},
                 Np::I, 
                 n_stab_W::I, 
                 n_stab_T::I, 
                 δW::E, 
                 δT::E, 
                 model_geometry::ModelGeometry, 
                 pht::Bool, 
                 rng::Xoshiro ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Attempts to move particle $\beta$ at lattice site $k$ to a randomly selected site $l$.

• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• jastrow_factor_1::JastrowFactor{E}: first Jastrow factor.
• jastrow_factor_2::JastrowFactor{E}: second Jastrow factor.
• jastrow_parameters_1::JastrowParameters{S, K, V, I}: first set of Jastrow parameters.
• jastrow_parameters_2::JastrowParameters{S, K, V, I}: second set of Jastrow parameters.
• Np::I: total number of particles in the system.
• n_stab_W::I: frequency of Green's function stabilization steps.
• n_stab_T::I: frequency of T vector stabilization steps.
• δW::E: error threshold for the Green's function.
• δT::E: error threshold for the T vector.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.
• rng::AbstractRNG: random number generator.

get_particle_density( density::E, 
                      model_geometry::ModelGeometry,
                      pht::Bool ) where {E<:AbstractFloat}

Given a particle density, returns the total number of particles $N_p$, the total number of electrons $N_e$ number of spin-up fermions $n_{\uparrow}$, number of spin-down fermions $n_{\downarrow}$. In cases where the given density is not a commensurate filling, a new density will be calculated to correspond with the new particle number.

• density::E: desired electronic density.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

get_particle_density( Np::I,
                      model_geometry::ModelGeometry,
                      pht::Bool ) where {I<:Integer}

Given the total number of particles in the lattice $N_p$, returns the particle density, the total number of electrons $N_e$, the number of spin-up fermions $n_{\uparrow}$ and the number of spin-down fermions $n_{\downarrow}$.

• Np::I: total number of particles.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

get_particle_density( nup::I, 
                      ndn::I,
                      model_geometry::ModelGeometry, 
                      pht::Bool ) where {I<:Integer}

Given the number of spin-up fermions $n_{\uparrow}$, and number of spin-down fermions $n_{\downarrow}$, returns the particle density, total number of particles $N_p$, and the total number of electrons $N_e$.

• nup::I: number of spin-up fermions.
• ndn::I: number of spin-down fermions.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

MarkovMove{I<:Integer}

A type defining a Markov process where a particle is proposed to moved from spindex $k$ to spindex $l$ and a Boolean denoting whether said move is possible.

• particle::I: the particle undergoing a Markov process.
• k::I: initial spindex of the particle.
• l::I: final spindex of the particle.
• possible::B: whether the Markov process is possible.

propose_random_move( Np::I, 
                     pconfig::AbstractVector{I}, 
                     model_geometry::ModelGeometry, 
                     rng::AbstractRNG ) where {I<:Integer}

Proposes randomly moving (via hopping or exchange) a particle from some intial spindex $k$ to a neighboring spindex $l$ and returns an instance of MarkovMove.

• Np::I: total number of particles in the system.
• pconfig::AbstractVector{I}: current particle configuration.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• rng::AbstractRNG: random number generator.

hop!( markov_move::MarkovMove{I}, 
      pconfig::AbstractVector{I} ) where {I<:Integer}

If a proposed move (hopping) is accepted, updates the particle positions in the currenrt configuration.

• markov_move::MarkovMove{I}: quantities related to a Markov process.
• pconfig::AbstractVector{I}: current particle configuration.

generate_initial_fermion_configuration!( pconfig::AbstractVector{I},
                                         nup::I, 
                                         ndn::I, 
                                         model_geometry::ModelGeometry, 
                                         rng::AbstractRNG ) where {I<:Integer}

Generates a random initial configuration of spin-up and spin-down fermions. The first N elements correspond to spin-up and the last N correspond to spin-down. Occupation is denoted by a positive integer corresponding to that particle's creation operator label.

• pconfig::Vector{I}: vector to store configurations.
• nup::I: number of spin-up fermions.
• ndn::I: number of spin-down fermions.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• rng::AbstractRNG: random number generator.

get_onsite_fermion_occupation( site::I, 
                               pconfig::AbstractVector{I},
                               N::I ) where {I<:Integer}

Returns the number of spin-up and spin-down fermions occupying a real lattice site i.

• site::I: lattice site.
• pconfig::AbstractVector{I}: current particle configuration.
• N::I: total number of sites.

get_spindex_type( spindex::I, 
                  model_geometry::ModelGeometry ) where {I<:Integer}

Returns the spin species at a given spindex.

• spindex::I: spin index.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

get_index_from_spindex( spindex::I, 
                        model_geometry::ModelGeometry ) where {I<:Integer}

Returns the lattice site $i$ for a given spindex.

• spindex::I: spin index.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

get_spindices_from_index( index::I, 
                          model_geometry::ModelGeometry ) where {I<:Integer}

Returns spin-up and spin-down indices from a given site index.

• index::I: lattice site index.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

get_linked_spindex( i::I, 
                    N::I ) where {I<:Integer}

Given an index $i$ in the spin-up sector, returns an index in the spin-down sector.

• i::I: lattice index in the spin-up sector.
• N::I: total number of lattice sites.

optimize_parameters!( measurement_container::NamedTuple, 
                      determinantal_parameters::DeterminantalParameters{I}, 
                      η::E, 
                      dt::E, 
                      bin_size::I ) where {I<:Integer, E<:AbstractFloat}

Optimizes and updates variational parameters using the Stochastic Reconfiguration method, in which the variation in parameter $\alpha_k$ can be found by solving $\delta\alpha_k = (S + \eta\mathbb{I})f^{-1}$, where $S$ is the covariance matrix, $f$ is the force vector, and $\eta$ is a stabilization parameter.

• measurement_container::NamedTuple: container where measurements are stored.
• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• η::E: optimization stabilization factor.
• dt::E: optimization rate.
• bin_size::I: length of the bins.

optimize_parameters!( measurement_container::NamedTuple, 
                      determinantal_parameters::DeterminantalParameters{I}, 
                      jastrow_parameters::JastrowParameters{T, K, V, I}, 
                      η::E, 
                      dt::E, 
                      dt_J::E,
                      bin_size::I ) where {I<:Integer, T<:AbstractString, K, V, E<:AbstractFloat}

Optimizes and updates variational parameters using the Stochastic Reconfiguration method, in which the variation in parameter $\alpha_k$ can be found by solving $\delta\alpha_k = (S + \eta\mathbb{I})f^{-1}$, where $S$ is the covariance matrix, $f$ is the force vector, and $\eta$ is a stabilization parameter.

• measurement_container::NamedTuple: container where measurements are stored.
• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• jastrow_parameters::JastrowParameters{T, K, V, I}: set of Jastrow variational parameters.
• η::E: optimization stabilization factor.
• dt::E: optimization rate.
• dt_J::E: boost in the optimization rate of the Jastrow parameters.
• bin_size::I: length of the bins.

optimize_parameters!( measurement_container::NamedTuple, 
                      determinantal_parameters::DeterminantalParameters{I}, 
                      jastrow_parameters_1::JastrowParameters{T, K, V, I},
                      jastrow_parameters_2::JastrowParameters{T, K, V, I}, 
                      η::E, 
                      dt::E, 
                      bin_size::I ) where {I<:Integer, T<:AbstractString, K, V, E<:AbstractFloat}

Optimizes and updates variational parameters using the Stochastic Reconfiguration method, in which the variation in parameter $\alpha_k$ can be found by solving $\delta\alpha_k = (S + \eta\mathbb{I})f^{-1}$, where $S$ is the covariance matrix, $f$ is the force vector, and $\eta$ is a stabilization parameter.

• measurement_container::NamedTuple: container where measurements are stored.
• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• jastrow_parameters_1::JastrowParameters{T, K, V, I}: set of Jastrow variational parameters.
• jastrow_parameters_2::JastrowParameters{T, K, V, I}: set of Jastrow variational parameters.
• η::E: optimization stabilization factor.
• dt::E: optimization rate.
• bin_size::I: length of the bins.

get_Δk( optimize::NamedTuple, 
        determinantal_parameters::DeterminantalParameters{I}, 
        detwf::DeterminantalWavefunction{T, V, E, I}, 
        model_geometry::ModelGeometry, 
        Np::I ) where {I<:Integer, T<:Number, V, E<:AbstractFloat}

Calculates the local logarithmic derivative $\Delta_k = \frac{\partial\ln\Psi_{T}}{\partial\alpha_k}$, for each determinantal variational parameter $\alpha_k$ and returns a vector of derivatives.

• optimize::NamedTuple: field of optimization flags.
• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• detwf::DeterminantalWavefunction{T, V, E, I}: current variational wavefunction.
• `model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• Np::I: total number of particles in the system.

get_Δk( optimize::NamedTuple, 
        jastrow_parameters::JastrowParameters{T, K, V, I},
        detwf::DeterminantalWavefunction{Q, F, E, I}, 
        pht::Bool ) where {T<:AbstractString, K, V, I<:Integer, Q<:Number, F, E<:AbstractFloat}

Calculates the local logarithmic derivative $\Delta_k = \frac{\partial\ln\Psi_{T}}{\partial\alpha_k}$, for each determinantal variational parameter $\alpha_k$ and returns a vector of derivatives.

• optimize::NamedTuple: field of optimization flags.
• jastrow_parameters::JastrowParameters{T, K, V, I}: current set of Jastrow variational parameters.
• detwf::DeterminantalWavefunction{Q, F, E, I}: current variational wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

get_covariance_matrix( measurement_container::NamedTuple, 
                       opt_bin_size::I ) where {I<:Integer}

Calculates the covariance matrix $S$ with elements $S_{kk}' = \langle \Delta_{k}\Delta_{k^\prime}\rangle - \langle \Delta_{k} \rangle\langle \Delta_{k^\prime} \rangle$.

• measurement_container::NamedTuple: container where measurements are stored.
• opt_bin_size::I: length of the current bin.

get_force_vector( measurement_container::NamedTuple, 
                  opt_bin_size::I ) where {I<:Integer}

Constructs force vector $f$ with elements $f_k = \langle \Delta_{k} \rangle\langle H\rangle - \langle \Delta_{k}H\rangle$.

• measurement_container::NamedTuple: container where measurements are stored.
• opt_bin_size::I: length of the current bin.

initialize_measurement_container( N_opt::I, 
                                  opt_bin_size::I, 
                                  N_sim::I, 
                                  sim_bin_size::I,
                                  determinantal_parameters::DeterminantalParameters{I}, 
                                  model_geometry::ModelGeometry ) where {I<:Integer}

Initializes a set of dictionaries containing generic arrays for storing measurements.

• N_opt::I: number of optimization updates.
• opt_bin_size::I: length of an optimization bin.
• N_sim::I: number of simulation bins.
• sim_bin_size::I: length of a simulation bin.
• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

initialize_measurement_container( N_opt::I, 
                                  opt_bin_size::I, 
                                  N_sim::I, 
                                  sim_bin_size::I,
                                  determinantal_parameters::DeterminantalParameters{I}, 
                                  jastrow_parameters::JastrowParameters{S, K, V, I},
                                  model_geometry::ModelGeometry ) where {I<:Integer, S<:AbstractString, K, V}

Initializes a set of dictionaries containing generic arrays for storing measurements.

• N_opt::I: number of optimization updates.
• opt_bin_size::I: length of an optimization bin.
• N_sim::I: number of simulation bins.
• sim_bin_size::I: length of a simulation bin.
• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• jastrow_parameters::JastrowParameters{S, K, V, I}: set of Jastrow variational parameters.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

initialize_measurement_container( N_opt::I, 
                                  opt_bin_size::I, 
                                  N_sim::I, 
                                  sim_bin_size::I,
                                  determinantal_parameters::DeterminantalParameters{I}, 
                                  jastrow_parameters_1::JastrowParameters{S, K, V, I},
                                  jastrow_parameters_2::JastrowParameters{S, K, V, I},
                                  model_geometry::ModelGeometry ) where {I<:Integer, S<:AbstractString, K, V}

Initializes a set of dictionaries containing generic arrays for storing measurements.

• N_opt::I: number of optimization updates.
• opt_bin_size::I: length of an optimization bin.
• N_sim::I: number of simulation bins.
• sim_bin_size::I: length of a simulation bin.
• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• jastrow_parameters_1::JastrowParameters{S, K, V, I}: first set of Jastrow variational parameters.
• jastrow_parameters_2::JastrowParameters{S, K, V, I}: second set of Jastrow variational parameters.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

initialize_measurement_directories(;
    simulation_info::SimulationInfo,
    measurement_container::NamedTuple
)

initialize_measurement_directories(
        comm::MPI.Comm;
        simulation_info::SimulationInfo,
        measurement_container::NamedTuple
)

initialize_measurement_directories(
    simulation_info::SimulationInfo,
    measurement_container::NamedTuple
)

initialize_measurement_directories(
        comm::MPI.Comm,
        simulation_info::SimulationInfo,
        measurement_container::NamedTuple
)

Initialize the measurement directories for simulation. If using MPI and a comm::MPI.Comm object is passed as the first argument, then none of the MPI processes will proceed beyond this function call until the measurement directories have been initialized.

get_local_energy( detwf::DeterminantalWavefunction{T, Q, E, I}, 
                  tight_binding_model::TightBindingModel{E}, 
                  model_geometry::ModelGeometry, 
                  U::E,
                  Np::I, 
                  pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Calculates the local variational energy $E_{\mathrm{var}}$ per site for a Hubbard model.

• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard interaction.
• Np::I: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

get_local_energy( detwf::DeterminantalWavefunction{T, Q, E, I}, 
                  tight_binding_model::TightBindingModel{E},
                  jastrow_parameters::JastrowParameters{S, K, V, I}, 
                  jastrow_factor::JastrowFactor{E},
                  model_geometry::ModelGeometry,
                  U::E,
                  Np::I,
                  pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Calculates the local variational energy $E_{\mathrm{var}}$ per site for a Hubbard model.

• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• jastrow_parameters::JastrowParameters{S, K, V, I}: current set of Jastrow variational parameters.
• jastrow_factor::JastrowFactor{E}: current Jastrow factor.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard interaction.
• Np::I: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

get_local_energy( detwf::DeterminantalWavefunction{T, Q, E, I}, 
                  tight_binding_model::TightBindingModel,
                  jastrow_parameters_1::JastrowParameters{S, K, V, I},
                  jastrow_parameters_2::JastrowParameters{S, K, V, I}, 
                  jastrow_factor_1::JastrowFactor{E},
                  jastrow_factor_2::JastrowFactor{E},
                  model_geometry::ModelGeometry,
                  U::E,
                  Np::I,
                  pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Calculates the local variational energy $E_{\mathrm{var}}$ per site for a Hubbard model.

• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• jastrow_parameters_1::JastrowParameters{S, K, V, I}: first set of Jastrow variational parameters.
• jastrow_parameters_2::JastrowParameters{S, K, V, I}: second set of Jastrow variational parameters.
• jastrow_factor_1::JastrowFactor{E}: first Jastrow factor.
• jastrow_factor_2::JastrowFactor{E}: second Jastrow factor.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard interaction.
• Np::I: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

get_local_kinetic_energy( detwf::DeterminantalWavefunction{T, Q, E, I}, 
                          tight_binding_model::TightBindingModel{E}, 
                          model_geometry::ModelGeometry, 
                          Np::I
                          pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Calculates the local kinetic energy $E_{\mathrm{kin}}$ .

• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• Np::I: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

get_local_kinetic_energy( detwf::DeterminantalWavefunction{T, Q, E, I}, 
                          tight_binding_model::TightBindingModel{E}, 
                          jastrow_parameters::JastrowParameters{S, K, V, I},
                          jastrow_factor::JastrowFactor{E}, 
                          model_geometry::ModelGeometry, 
                          Np::I,
                          pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Calculates the local kinetic energy $E_{\mathrm{kin}}$ .

• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• jastrow_parameters::JastrowParameters{S, K, V, I}: current set of Jastrow variational parameters.
• jastrow_factor::JastrowFactor{E}: current Jastrow factor.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• Np::I: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

get_local_kinetic_energy( detwf::DeterminantalWavefunctionT, Q, E, I}, 
                          tight_binding_model::TightBindingModel{E}, 
                          jastrow_parameters_1::JastrowParameters{S, K, V, I},
                          jastrow_parameters_2::JastrowParameters{S, K, V, I},
                          jastrow_factor_1::JastrowFactor{E},
                          jastrow_factor_2::JastrowFactor{E}, 
                          model_geometry::ModelGeometry, 
                          Np::I,
                          pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Calculates the local kinetic energy $E_{\mathrm{kin}}$ .

• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• jastrow_parameters_1::JastrowParameters{S, K, V, I}: first set of Jastrow variational parameters.
• jastrow_parameters_2::JastrowParameters{S, K, V, I}: second set of Jastrow variational parameters.
• jastrow_factor_1::JastrowFactor{E}: first Jastrow factor.
• jastrow_factor_2::JastrowFactor{E}: second Jastrow factor.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• Np::I: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

get_local_hubbard_energy( U::E, 
                          detwf::DeterminantalWavefunction{T, Q, E, I}, 
                          model_geometry::ModelGeometry, 
                          pht::Bool ) where {E<:AbstractFloat, T<:Number, Q, I<:Integer}

Calculates the energy due to on-site Hubbard interaction $U$.

• U::E: Hubbard interaction.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

get_double_occ( detwf::DeterminantalParameters{T, Q, E, I}, 
                model_geometry::ModelGeometry, 
                pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Calculates the average double occupancy$D = \sum_{i} n_{\boldsymbol{i},\uparrow}n_{\boldsymbol{i},\downarrow}$.

• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

get_n( detwf::DeterminantalWavefunction{T, Q, E, I}, 
       model_geometry::ModelGeometry,
       pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Calculate the average particle density $n = \sum_{i} (n_{\boldsymbol{i},\uparrow} + n_{\boldsymbol{i},\downarrow})$.

• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

get_Sz( detwf::DeterminantalWavefunction{T, Q, E, I}, 
        model_geometry::ModelGeometry,
        pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Calculate the average value of the operator $S_z = \frac{1}{2} \sum_{i} (n_{\boldsymbol{i},\uparrow} - n_{\boldsymbol{i},\downarrow})$.

• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

measure_Δk!( measurement_container::NamedTuple, 
             detwf::DeterminantalWavefunction{T, Q, E, I}, 
             determinantal_parameters::DeterminantalParameters{I}, 
             optimize::NamedTuple,
             model_geometry::ModelGeometry, 
             Np::I ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Measures the logarithmic derivative $\Delta_k$ for $k$ variational parameters and then writes them to the measurement container.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• determinantal_parameters::DeterminantalParameters{I}: current set of determinantal variational parameters.
• optimize::NamedTuple:: tuple of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• Np::I: total number of particles in the system.

measure_Δk!( measurement_container::NamedTuple, 
             detwf::DeterminantalWavefunction{T, Q, E, I}, 
             determinantal_parameters::DeterminantalParameters{I}, 
             jastrow_parameters::JastrowParameters{S, K, V, I}, 
             optimize::NamedTuple,
             model_geometry::ModelGeometry, 
             Np::I, 
             pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Measures the logarithmic derivative $\Delta_k$ for `k variational parameters and then writes them to the measurement container.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• determinantal_parameters::DeterminantalParameters: current set of determinantal variational parameters.
• jastrow_parameters::JastrowParameters{S, K, V, I}: first set of Jastrow variational parameters.
• optimize::NamedTuple:: tuple of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• Np::I: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

measure_Δk!( measurement_container::NamedTuple, 
             detwf::DeterminantalWavefunction{T, Q, E, I}, 
             determinantal_parameters::DeterminantalParameters{I}, 
             jastrow_parameters_1::JastrowParameters{S, K, V, I},
             jastrow_parameters_2::JastrowParameters{S, K, V, I},
             optimize::NamedTuple,
             model_geometry::ModelGeometry, 
             Np::I, 
             pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Measures the logarithmic derivative $\Delta_k$ for `k variational parameters and then writes them to the measurement container.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction: current variational wavefunction.
• determinantal_parameters::DeterminantalParameters: current set of determinantal variational parameters.
• jastrow_parameters_1::JastrowParameters: first set of Jastrow variational parameters.
• jastrow_parameters_2::JastrowParameters: second set of Jastrow variational parameters.
• optimize::NamedTuple:: tuple of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• Np::Int: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

measure_ΔkΔkp!( measurement_container::NamedTuple, 
                detwf::DeterminantalWavefunction{T, Q, E, I}, 
                determinantal_parameters::DeterminantalParameters{I}, 
                optimize::NamedTuple,
                model_geometry::ModelGeometry, 
                Np::I ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Measures the product of logarithmic derivatives $\Delta_{k}\Delta_{k}^\prime$ and then writes them to the measurement container.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction: current variational wavefunction.
• determinantal_parameters::DeterminantalParameters: current variational determinantal parameters.
• optimize::NamedTuple:: tuple of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• Np::Int: total number of particles in the system.

measure_ΔkΔkp!( measurement_container::NamedTuple, 
                detwf::DeterminantalWavefunction{T, Q, E, I}, 
                determinantal_parameters::DeterminantalParameters{I}, 
                jastrow_parameters::JastrowParameters{S, K, V, I},
                optimize::NamedTuple,
                model_geometry::ModelGeometry, 
                Np::I, 
                pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Measures the product of logarithmic derivatives $\Delta_{k}\Delta_{k}^\prime$ and then writes them to the measurement container.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction: current variational wavefunction.
• determinantal_parameters::DeterminantalParameters: current set of determinantal variational parameters.
• jastrow_parameters::JastrowParameters: current set of Jastrow variational parameters.
• optimize::NamedTuple:: tuple of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• Np::Int: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

measure_ΔkΔkp!( measurement_container::NamedTuple, 
                detwf::DeterminantalWavefunction{T, Q, E, I}, 
                determinantal_parameters::DeterminantalParameters{I}, 
                jastrow_parameters_1::JastrowParameters{S, K, V, I},
                jastrow_parameters_2::JastrowParameters{S, K, V, I},
                optimize::NamedTuple,
                model_geometry::ModelGeometry, 
                Np::I, 
                pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Measures the product of logarithmic derivatives $\Delta_{k}\Delta_{k}^\prime$ and then writes them to the measurement container.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction: current variational wavefunction.
• determinantal_parameters::DeterminantalParameters: current set of determinantal variational parameters.
• jastrow_parameters_1::JastrowParameters: first set of Jastrow variational parameters.
• jastrow_parameters_2::JastrowParameters: second set of Jastrow variational parameters.
• optimize::NamedTuple:: tuple of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• Np::Int: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

measure_ΔkE!( measurement_container::NamedTuple, 
              detwf::DeterminantalWavefunction{T, Q, E, I}, 
              tight_binding_model::TightBindingModel{E}, 
              determinantal_parameters::DeterminantalParameters{I}, 
              optimize::NamedTuple,
              model_geometry::ModelGeometry, 
              U::E,
              Np::I, 
              pht::Bool )where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Measures the product of logarithmic derivatives with the local energy $\Delta_{k}E$ and then writes them to the measurement container.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction: current variational wavefunction.
• tight_binding_model::TightBindingModel: parameter for a non-interacting tight-binding model.
• determinantal_parameters::DeterminantalParameters: current set of determinantal variational parameters.
• optimize::NamedTuple:: tuple of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard repulsion.
• Np::Int: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

measure_ΔkE!( measurement_container::NamedTuple, 
              detwf::DeterminantalWavefunction{T, Q, E, I}, 
              tight_binding_model::TightBindingModel{E}, 
              determinantal_parameters::DeterminantalParameters{I}, 
              jastrow_parameters::JastrowParameters{S, K, V, I}, 
              jastrow_factor::JastrowFactor{E, I},
              optimize::NamedTuple,
              model_geometry::ModelGeometry, 
              U::E,
              Np::I, 
              pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Measures the product of logarithmic derivatives with the local energy $\Delta_{k}E$ and then writes them to the measurement container.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction: current variational wavefunction.
• tight_binding_model::TightBindingModel: parameters for a non-interacting tight-binding model.
• determinantal_parameters::DeterminantalParameters: current set of determinantal variational parameters.
• jastrow_parameters::JastrowParameters: current set of Jastrow variational parameters.
• jastrow_factor::JastrowFactor: current Jastrow factor.
• optimize::NamedTuple:: tuple of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard repulsion.
• Np::Int: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

measure_ΔkE!( measurement_container::NamedTuple, 
              detwf::DeterminantalWavefunction{T, Q, E, I}, 
              tight_binding_model::TightBindingModel{E}, 
              determinantal_parameters::DeterminantalParameters{I}, 
              jastrow_parameters_1::JastrowParameters{S, K, V, I},
              jastrow_parameters_2::JastrowParameters{S, K, V, I}, 
              jastrow_factor_1::JastrowFactor{E, I},
              jastrow_factor_2::JastrowFactor{E, I},
              optimize::NamedTuple,
              model_geometry::ModelGeometry, 
              U::E,
              Np::I, 
              pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Measures the product of logarithmic derivatives with the local energy $\Delta_{k}E$ and then writes them to the measurement container.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction: current variational wavefunction.
• tight_binding_model::TightBindingModel: parameters for a non-interacting tight-binding model.
• determinantal_parameters::DeterminantalParameters: current set of determinantal variational parameters.
• jastrow_parameters_1::JastrowParameters: first set of Jastrow variational parameters.
• jastrow_parameters_2::JastrowParameters: second set of Jastrow variational parameters.
• jastrow_factor_1::JastrowFactor: first Jastrow factor.
• jastrow_factor_2::JastrowFactor: second Jastrow factor.
• optimize::NamedTuple:: tuple of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard repulsion.
• Np::Int: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

measure_local_energy!( measurement_container::NamedTuple, 
                       detwf::DeterminantalWavefunction{T, Q, E, I}, 
                       tight_binding_model::TightBindingModel{E}, 
                       model_geometry::ModelGeometry,
                       U::E,
                       Np::I,
                       pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Measures the total local energy $E_{\mathrm{loc}}$ for a Hubbard model and writes to the measurement container.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard interaction.
• Np::I: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

measure_local_energy!( measurement_container::NamedTuple, 
                       detwf::DeterminantalWavefunction{T, Q, E, I}, 
                       tight_binding_model::TightBindingModel{E}, 
                       jastrow_parameters::JastrowParameters{S, K, V, I},
                       jastrow_factor::JastrowFactor{E}, 
                       model_geometry::ModelGeometry,
                       U::E,
                       Np::I, 
                       pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Measures the total local energy $E_{\mathrm{loc}}$ for a Hubbard model and writes to the measurement container.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• jastrow_parameters::JastrowParameters{S, K, V, I}: current set of Jastrow variational parameters.
• jastrow_factor::JastrowFactor{E}: current Jastrow factor.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard interaction.
• Np::I: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

measure_local_energy!( measurement_container::NamedTuple, 
                       detwf::DeterminantalWavefunction{T, Q, E, I}, 
                       tight_binding_model::TightBindingModel{E}, 
                       jastrow_parameters_1::JastrowParameters{S, K, V, I},
                       jastrow_parameters_2::JastrowParameters{S, K, V, I},
                       jastrow_factor_1::JastrowFactor{E},
                       jastrow_factor_2::JastrowFactor{E}, 
                       model_geometry::ModelGeometry,
                       U::E,
                       Np::I, 
                       pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Measures the total local energy $E_{\mathrm{loc}}$ for a Hubbard model and writes to the measurement container.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• tight_binding_model::TightBindingModel{E}: parameters for a non-interacting tight-binding model.
• jastrow_parameters_1::JastrowParameters{S, K, V, I}: first set of Jastrow variational parameters.
• jastrow_parameters_2::JastrowParameters{S, K, V, I}: second set of Jastrow variational parameters.
• jastrow_factor_1::JastrowFactor{E}: first Jastrow factor.
• jastrow_factor_2::JastrowFactor{E}: second Jastrow factor.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard interaction.
• Np::I: total number of particles in the system.
• pht::Bool: whether model is particle-hole transformed.

measure_double_occ!( measurement_container::NamedTuple, 
                     detwf::DeterminantalWavefunction{T, Q, E, I}, 
                     model_geometry::ModelGeometry, 
                     pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Measures the average double occupancy $\langle D\rangle$.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

measure_n!( type::String,
            measurement_container::NamedTuple, 
            detwf::DeterminantalWavefunction{T, Q, E, I}, 
            model_geometry::ModelGeometry,
            pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Measures the local or site-dependent particle density averaged over all sites $\langle n\rangle$.

• type::String: type of measurement. Either "local" or "site-dependent".
• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

measure_Sz!( type::String,
             measurement_container::NamedTuple, 
             detwf::DeterminantalWavefunction{T, Q, E, I}, 
             model_geometry::ModelGeometry,
             pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Measures the local or site-dependent spin z-component over averaged all sites $\langle S_z\rangle$.

• type::String: type of measurement. Either "local" or "site-dependent".
• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

measure_density_correlation!( measurement_container::NameTuple,
                              detwf::DeterminantalWavefunction{T, Q, E, I},
                              model_geometry::ModelGeometry,
                              pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Measures the equal-time density-density correlation function $\langle \hat{n}_{i}\hat{n}_{j}\rangle$.

• measurement_container::NamedTuple: container where measurements are stroed.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transform.

measure_spin_correlation!( measurement_container::NamedTuple,
                           detwf::DeterminantalWavefunction{T, Q, E, I},
                           model_geometry::ModelGeometry,
                           pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Measures the equal-time spin-spin correlation function $\langle \hat{S}_{i}\hat{S}_{j}\rangle$.

• measurement_container::NamedTuple: container where measurements are stroed.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transform.

get_site_dependent_n( detwf::DeterminantalWavefunction{T, Q, E, I}, 
                      model_geometry::ModelGeometry,
                      pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Calculates the local density $n_{\boldsymbol{i}}$ on each lattice site.

• detwf::DeterminantalWavefunction{T, Q, E, I}: current variational wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

get_site_dependent_s( detwf::DeterminantalParameters{T, Q, E, I}
                      model_geometry::ModelGeometry,
                      pht::Bool )

Calculates the local spin $S_{\boldsymbol{i}}$ on each lattice site.

• detwf::DeterminantalParameters{T, Q, E, I}: current variational wavefunction.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• pht::Bool: whether model is particle-hole transformed.

make_measurements!( measurement_container::NamedTuple, 
                    detwf::DeterminantalWavefunction{T, Q, E, I}, 
                    tight_binding_model::TightBindingModel{E}, 
                    determinantal_parameters::DeterminantalParameters{I}, 
                    optimize::NamedTuple,
                    model_geometry::ModelGeometry,
                    U::E,
                    Np::I, 
                    pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Measures optimization and simulation observables including the local energy $\langle E_{\mathrm{loc}}\rangle$, logarithmic derivatives $\langle\Delta_k\rangle$, $\langle\Delta_{k}\Delta_{k}^\prime\rangle$, $\langle\Delta_{k}E\rangle$, average double occupancy $\langle D\rangle$, and average density $\langle n\rangle$. Also records the current particle configuration $|x\rangle$.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current determinantal wavefunction.
• tight_binding_model::TightBindingModel{E}: non-interacting tight-binding model.
• determinantal_parameters{I}::DeterminantalParameters{I}: set of determinantal variational parameters.
• optimize::NamedTuple:: tuple of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard interaction.
• Np::I: total number of particles in the system.
• pht::Bool: whether or not model is particle-hole transformed.

make_measurements!( measurement_container::NamedTuple, 
                    detwf::DeterminantalWavefunction{T, Q, E, I}, 
                    tight_binding_model::TightBindingModel{E},
                    determinantal_parameters::DeterminantalParameters{I},
                    jastrow_parameters::JastrowParameters{S, K, V, I},
                    jastrow_factor::JastrowFactor{E, I},
                    optimize::NamedTuple,
                    model_geometry::ModelGeometry, 
                    U::E,
                    Np::I, 
                    pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Measures optimization and simulation observables including the local energy $\langle E_{\mathrm{loc}}\rangle$, logarithmic derivatives $\langle\Delta_k\rangle$, $\langle\Delta_{k}\Delta_{k}^\prime\rangle$, $\langle\Delta_{k}E\rangle$, average double occupancy $\langle D\rangle$, and average density $\langle n\rangle$. Also records the current particle configuration $|x\rangle$.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current determinantal wavefunction.
• tight_binding_model::TightBindingModel{E}: non-interacting tight-binding model.
• determinantal_parameters::DeterminantalParameters{I}: set of determinantal variational parameters.
• jastrow_parameters::JastrowParameters{S, K, V, I}: current set of Jastrow variational parameters.
• jastrow_factor::JastrowFactor{E, I}: current Jastrow factor.
• optimize::NamedTuple:: tuple of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard interaction.
• Np::I: total number of particles in the system.
• pht::Bool: whether or not model is particle-hole transformed.

make_measurements!( measurement_container::NamedTuple, 
                    detwf::DeterminantalWavefunction{T, Q, E, I}, 
                    tight_binding_model::TightBindingModel{E},
                    determinantal_parameters::DeterminantalParameters{I},
                    jastrow_parameters_1::JastrowParameters{S, K, V, I},
                    jastrow_parameters_2::JastrowParameters{S, K, V, I},
                    jastrow_factor_1::JastrowFactor{E, I},
                    jastrow_factor_2::JastrowFactor{E, I}, 
                    optimize::NamedTuple,
                    model_geometry::ModelGeometry, 
                    U::E,
                    Np::I, 
                    pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Measures optimization and simulation observables including the local energy $\langle E_{\mathrm{loc}}\rangle$, logarithmic derivatives $\langle\Delta_k\rangle$, $\langle\Delta_{k}\Delta_{k}^\prime\rangle$, $\langle\Delta_{k}E\rangle$, average double occupancy $\langle D\rangle$, and average density $\langle n\rangle$. Also records the current particle configuration $|x\rangle$.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current determinantal wavefunction.
• tight_binding_model::TightBindingModel{E}: non-interacting tight-binding model.
• determinantal_parameters::DeterminantalParameters: set of determinantal variational parameters.
• jastrow_parameters_1::JastrowParameters{S, K, V, I}: first set of Jastrow variational parameters.
• jastrow_parameters_2::JastrowParameters{S, K, V, I}: second set of Jastrow variational parameters.
• jastrow_factor_1::JastrowFactor{E, I}: first Jastrow factor.
• jastrow_factor_2::JastrowFactor{E, I}: second Jastrow factor.
• optimize::NamedTuple:: tuple of optimization flags.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard interaction.
• Np::I: total number of particles in the system.
• pht::Bool: whether or not model is particle-hole transformed.

make_measurements!( measurement_container::NamedTuple, 
                    detwf::DeterminantalWavefunction{T, Q, E, I}, 
                    tight_binding_model::TightBindingModel{E}, 
                    model_geometry::ModelGeometry, 
                    U::E,
                    Np::I, 
                    pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer}

Measures simulation observables including the local energy $\langle E_{\mathrm{loc}}\rangle$, average double occupancy $\langle D\rangle$, and average density $\langle n\rangle$. Also records the current particle configuration $|x\rangle$.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current determinantal wavefunction.
• tight_binding_model::TightBindingModel{E}: non-interacting tight-binding model.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard interaction.
• Np::I: total number of particles in the system.
• pht::Bool: whether or not model is particle-hole transformed.

make_measurements!( measurement_container::NamedTuple, 
                    detwf::DeterminantalWavefunction{T, Q, E, I}, 
                    tight_binding_model::TightBindingModel{E}, 
                    jastrow_parameters::JastrowParameters{S, K, V, I},
                    jastrow_factor::JastrowFactor{E}, 
                    model_geometry::ModelGeometry, 
                    U::E,
                    Np::I, 
                    pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Measures simulation observables including the local energy $\langle E_{\mathrm{loc}}\rangle$, average double occupancy $\langle D\rangle$, and average density $\langle n\rangle$. Also records the current particle configuration $|x\rangle$.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current determinantal wavefunction.
• tight_binding_model::TightBindingModel{E}: non-interacting tight-binding model.
• jastrow_parameters::JastrowParameters{S, K, V, I}: current set of Jastrow variational parameters.
• jastrow_factor::JastrowFactor{E}: current Jastrow factor.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard interaction.
• Np::I: total number of particles in the system.
• pht::Bool: whether or not model is particle-hole transformed.

make_measurements!( measurement_container::NamedTuple, 
                    detwf::DeterminantalWavefunction{T, Q, E, I}, 
                    tight_binding_model::TightBindingModel{E}, 
                    jastrow_parameters_1::JastrowParameters{S, K, V, I},
                    jastrow_parameters_2::JastrowParameters{S, K, V, I},
                    jastrow_factor_1::JastrowFactor{E},
                    jastrow_factor_2::JastrowFactor{E}, 
                    model_geometry::ModelGeometry, 
                    U::E,
                    Np::I, 
                    pht::Bool ) where {T<:Number, Q, E<:AbstractFloat, I<:Integer, S<:AbstractString, K, V}

Measures simulation observables including the local energy $\langle E_{\mathrm{loc}}\rangle$, average double occupancy $\langle D\rangle$, and average density $\langle n\rangle$. Also records the current particle configuration $|x\rangle$.

• measurement_container::NamedTuple: container where measurements are stored.
• detwf::DeterminantalWavefunction{T, Q, E, I}: current determinantal wavefunction.
• tight_binding_model::TightBindingModel{E}: non-interacting tight-binding model.
• jastrow_parameters_1::JastrowParameters{S, K, V, I}: first set of Jastrow variational parameters.
• jastrow_parameters_2::JastrowParameters{S, K, V, I}: second set of Jastrow variational parameters.
• jastrow_factor_1::JastrowFactor{E}: first Jastrow factor.
• jastrow_factor_2::JastrowFactor{E}: second Jastrow factor.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.
• U::E: Hubbard interaction.
• Np::I: total number of particles in the system.
• pht::Bool: whether or not model is particle-hole transformed.

reset_measurements!( measurements::Dict{S, T}; 
                     in_place::Bool = false ) where {S<:AbstractString, T}

Resets values in the measurement container to zero.

• measurements::Dict{S, T}: measurement container.
• in_place::Bool = false: whether to perform in-place update of measurements. Best to set to false to prevent undesired mutation.

write_measurements!( step::AbstractString
                     bin::I, 
                     bin_size::I,
                     measurement_container::NamedTuple, 
                     simulation_info::SimulationInfo;
                     write_parameters=false ) where {I<:Integer}

Writes simulation and correlation (if measured) measurements in the current bin to file. Files created are in HDF5 format.

• step::AbstractString: VMC step: opt or sim, optimization or simulation.
• bin::I: current bin.
• bin_size::I: size of the current bins.
• measurement_container::NamedTuple: container where measurements are stored.
• simulation_info::SimulationInfo: contains datafolder names.
• write_parameters=false: whether parameters are written to file. Set to true during optimization.

Data in each file can be accessed by doing:

h5open(simfile, "r") do f # list all top-level measurements println(keys(f)) # e.g., ["globaldensity", "double_occ", ...]

# access a specific dataset
data = read(f["/local_energy/bin-1/"])  # returns a Julia array
println(data)

end

for num in 1:Noptbins h5open(opt_file, "r") do f data = read(f["/parameters/bin-num/"]) println(data) end end

normalize_measurements( data, 
                        bin_size::I, 
                        key::AbstractString )

Normalizes different types of data by the length of a bin.

• data: data of abstract type.
• bin_size::I: length of the bin.
• key::AbstractString: name of measurement.

process_measurements( measurement_container::NamedTuple,
                      simulation_info::SimulationInfo,
                      determinantal_parameters::DeterminantalParameters,
                      model_geometry::ModelGeometry )

Processes all simulation and optimization measurements by organinzing them into CSV files.

• measurement_container::NamedTuple: contains measurement quantities.
• simulation_info::SimulationInfo: contains all simulation info.
• determinantal_parameters::DeterminantalParameters: set of determinantal variational parameters.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

process_measurements( measurement_container::NamedTuple,
                      simulation_info::SimulationInfo,
                      determinantal_parameters::DeterminantalParameters,
                      jastrow_parameters::JastrowParameters,
                      model_geometry::ModelGeometry )

Processes all simulation and optimization measurements by organinzing them into CSV files.

• measurement_container::NamedTuple: contains measurement quantities.
• simulation_info::SimulationInfo: contains all simulation info.
• determinantal_parameters::DeterminantalParameters: set of determinantal variational parameters.
• jastrow_parameters::JastrowParameters: set of Jastrow parameters.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

process_measurements( measurement_container::NamedTuple,
                      simulation_info::SimulationInfo,
                      determinantal_parameters::DeterminantalParameters,
                      jastrow_parameters_1::JastrowParameters,
                      jastrow_parameters_2::JastrowParameters,
                      model_geometry::ModelGeometry )

Processes all simulation and optimization measurements by organinzing them into CSV files.

• measurement_container::NamedTuple: contains measurement quantities.
• simulation_info::SimulationInfo: contains all simulation info.
• determinantal_parameters::DeterminantalParameters: set of determinantal variational parameters.
• jastrow_parameters_1::JastrowParameters: first set of Jastrow parameters.
• jastrow_parameters_2::JastrowParameters: second set of Jastrow parameters.
• model_geometry::ModelGeometry: contains unit cell and lattice quantities.

process_scalar_measurements( datafolder::T,
                             pID::I,
                             measurement::T;
                             N_bins::Union{I, Nothing}=nothing;
                             bins_to_avg::Union{I, Nothing}=nothing ) where {T<:AbstractString, I<:Integer}

Write binned simulation measurements to CSV.

• datafolder::T: path to folder where simulation files are written.
• pID::I: processor ID/MPI rank
• measurement::T: "localenergy", "doubleocc", "globaldensity", "site-dependentdensity", "pconfig", "localspin-z", or "site-dependentspin-z".
• N_bins::Union{I, Nothing}=nothing: (optional) total number of bins.
• bins_to_avg::Union{I, Nothing}=nothing: number of bins to average over when performing jackknife resampling.

process_optimization_measurements( datafolder::T,
                                   pID::I,
                                   determinantal_parameters::DeterminantalParameters;
                                   N_bins::Union{I, Nothing}=nothing ) where {T<:AbstractString, I<:Integer}

Writes binned optimization measurements to CSV.

• datafolder::T: path to folder where simulation files are written.
• pID::I: processor ID/MPI rank
• determinantal_parameters::DeterminantalParameters: set of determinantal variational parameters.
• N_bins::Union{I, Nothing}=nothing: (optional) total number of bins.

process_optimization_measurements( datafolder::T,
                                   pID::I,
                                   determinantal_parameters::DeterminantalParameters,
                                   jastrow_parameters::JastrowParameters;
                                   N_bins::Union{I, Nothing}=nothing ) where {T<:AbstractString, I<:Integer}

Writes binned optimization measurements to CSV.

• datafolder::T: path to folder where simulation files are written.
• pID::I: processor ID/MPI rank
• determinantal_parameters::DeterminantalParameters: set of determinantal variational parameters.
• jastrow_parameters::JastrowParameters: set of Jastrow parameters.
• N_bins::Union{I, Nothing}=nothing: (optional) total number of bins.

process_optimization_measurements( datafolder::T,
                                   pID::I,
                                   determinantal_parameters::DeterminantalParameters,
                                   jastrow_parameters_1::JastrowParameters,
                                   jastrow_parameters_2::JastrowParameters;
                                   N_bins::Union{I, Nothing}=nothing ) where {T<:AbstractString, I<:Integer}

Writes binned optimization measurements to CSV.

• datafolder::T: path to folder where simulation files are written.
• pID::I: processor ID/MPI rank
• determinantal_parameters::DeterminantalParameters: set of determinantal variational parameters.
• jastrow_parameters_1::JastrowParameters: first set of Jastrow parameters.
• jastrow_parameters_2::JastrowParameters: second set of Jastrow parameters.
• N_bins::Union{I, Nothing}=nothing: (optional) total number of bins.