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

James Stokes,Javier Robledo Moreno,Eftychios A Pnevmatikakis,Giuseppe Carleo

doi:10.1103/physrevb.102.205122

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.

Highlights

The difficulty in treating interacting quantum systems stems directly from the fact that the state space of a manybody quantum system grows exponentially with the number of its constituents
The prevailing paradigm for simulating lattice quantum systems in one spatial dimension is the density-matrix renormalization group (DMRG) [1,2], which involves an iterative procedure to approximate low-entanglement quantum states using representations known as matrix product states [3,4]
We focus on the problem of approximating the ground state for a model of two-dimensional spinless fermions with nearestneighbor interactions, modeling the wave function using a Slater-Jastrow-inspired factorization [19], with an additional neural network trained to capture sign deviations [20] compared with the Slater determinant

Summary

Introduction

The difficulty in treating interacting quantum systems stems directly from the fact that the state space of a manybody quantum system grows exponentially with the number of its constituents. When many-body effects are dominant, variational methods have proven a successful strategy to approximately represent, in a compact and computationally manageable form, many-body quantum states. The prevailing paradigm for simulating lattice quantum systems in one spatial dimension is the density-matrix renormalization group (DMRG) [1,2], which involves an iterative procedure to approximate low-entanglement quantum states using representations known as matrix product states [3,4]. The success of DMRG to produce high overlap with the ground space stems from the ability of matrix product states to approximate gapped one-dimensional quantum systems [5] and the existence of a very efficient numerical scheme for their variational optimization. In two or more spatial dimensions, the situation is qualitatively very different and research into both computationally efficient and compact

Methods

Results

Conclusion