Fermionic Wave Functions from Neural-Network Constrained Hidden States

TL;DR

This paper introduces a flexible neural-network-based variational wave function for simulating strongly correlated fermionic systems, achieving high accuracy in Hubbard model ground state calculations.

Contribution

It presents a novel neural-network constrained hidden state approach that overcomes previous limitations and is proven to be universal for fermionic wave functions.

Findings

Achieves state-of-the-art accuracy in Hubbard model simulations

Provides an extremely expressive and universal wave function family

Overcomes mean-field limitations of previous hidden particle methods

Abstract

We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving "hidden" additional fermionic degrees of freedom. These determinants are projected onto the physical Hilbert space through a constraint which is optimized, together with the single-particle orbitals, using a neural network parametrization. This construction draws inspiration from the success of hidden particle representations but overcomes the limitations associated with the mean-field treatment of the constraint often used in this context. Our construction provides an extremely expressive family of wave functions, which is proven to be universal. We apply this construction to the ground state properties of the Hubbard model on the square lattice, achieving levels of accuracy which are competitive with state-of-the-art variational methods.