Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states

TL;DR

This paper introduces a deep neural network approach for analyzing strongly interacting spinless fermions on a lattice, achieving high accuracy in ground state properties and phase boundary estimates.

Contribution

Develops a first-quantized deep neural network method with a Slater-Jastrow inspired ansatz for lattice fermions, improving accuracy over traditional techniques.

Findings

Accurately determines ground states and correlation functions for small systems.

Provides phase boundary estimates between metallic and charge-ordered phases.

Achieves high accuracy in large system simulations.

Abstract

First-quantized deep neural network techniques are developed for analyzing strongly coupled fermionic systems on the lattice. Using a Slater-Jastrow inspired ansatz which exploits deep residual networks with convolutional residual blocks, we approximately determine the ground state of spinless fermions on a square lattice with nearest-neighbor interactions. The flexibility of the neural-network ansatz results in a high level of accuracy when compared to exact diagonalization results on small systems, both for energy and correlation functions. On large systems, we obtain accurate estimates of the boundaries between metallic and charge ordered phases as a function of the interaction strength and the particle density.