Source code for netket.models.slater

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import flax.linen as nn
import jax.numpy as jnp

from functools import partial

import numpy as np

from netket.experimental.hilbert import SpinOrbitalFermions
from netket.utils.types import NNInitFunc, DType
from netket.nn.masked_linear import default_kernel_init
from netket import jax as nkjax

[docs] class Slater2nd(nn.Module): r""" A slater determinant ansatz for second-quantised spinless or spin-full fermions. The log-determinants of every spin sub-sector are summed together. The total number of parameters of this ansatz is :math:`n_{\mathrm{o}} \times n_{\mathrm{f}}`, where :math:`n_{\mathrm{o}}` is the number of orbitals and :math:`n_{\mathrm{f}}` is the total number of fermions in the system. """ hilbert: SpinOrbitalFermions """The Hilbert space upon which this ansatz is defined. Used to determine the number of orbitals and spin subspectors.""" restricted: bool = True """Flag to select the restricted- or unrestricted- Hartree Fock orbtals (Defaults to restricted). If restricted, only one set of orbitals are parametrised, and they are used for all spin subsectors. If unrestricted, a different set of orbitals are parametrised and used for each spin subsector. """ kernel_init: NNInitFunc = default_kernel_init """Initializer for the orbital parameters.""" param_dtype: DType = float """Dtype of the orbital amplitudes.""" def __post_init__(self): if not isinstance(self.hilbert, SpinOrbitalFermions): raise TypeError( "Slater2nd only supports 2nd quantised fermionic hilbert spaces." ) if self.hilbert.n_fermions is None: raise TypeError( "Slater2nd only supports hilbert spaces with a " "fixed number of fermions." ) if self.restricted: if not all( np.equal( self.hilbert.n_fermions_per_spin, self.hilbert.n_fermions_per_spin[0], ) ): raise ValueError( "Restricted Hartree Fock only makes sense for spaces with " "same number of fermions on every subspace." ) super().__post_init__() def setup(self): # Every determinant is a matrix of shape (n_orbitals, n_fermions_i) where # n_fermions_i is the number of fermions in the i-th spin sector. if self.restricted: M = self.param( "M", self.kernel_init, (self.hilbert.n_orbitals, self.hilbert.n_fermions_per_spin[0]), self.param_dtype, ) self.orbitals = [M for _ in self.hilbert.n_fermions_per_spin] else: self.orbitals = [ self.param( f"M_{i}", self.kernel_init, (self.hilbert.n_orbitals, nf_i), self.param_dtype, ) for i, nf_i in enumerate(self.hilbert.n_fermions_per_spin) ]
[docs] def __call__(self, n): """ Assumes inputs are strings of 0,1 that specify which orbitals are occupied. Spin sectors are assumed to follow the SpinOrbitalFermion's factorisation, meaning that the first `n_orbitals` entries correspond to sector -1, the second `n_orbitals` correspond to 0 ... etc. """ if not n.shape[-1] == self.hilbert.size: raise ValueError( f"Dimension mismatch. Expected samples with {self.hilbert.size} " f"degrees of freedom, but got a sample of shape {n.shape} ({n.shape[-1]} dof)." ) @partial(jnp.vectorize, signature="(n)->()") def log_sd(n): # Find the positions of the occupied sites R = n.nonzero(size=self.hilbert.n_fermions)[0] log_det_sum = 0 i_start = 0 for i, (n_fermions_i, M_i) in enumerate( zip(self.hilbert.n_fermions_per_spin, self.orbitals) ): # convert global orbital positions to spin-sector-local positions R_i = R[i_start : i_start + n_fermions_i] - i * self.hilbert.n_orbitals # extract the corresponding Nf x Nf submatrix A_i = M_i[R_i] log_det_sum = log_det_sum + nkjax.logdet_cmplx(A_i) i_start = n_fermions_i return log_det_sum return log_sd(n)