Approximating quantum many-body wave-functions using artificial neural networks

TL;DR

This paper shows that simple feed-forward neural networks can accurately approximate ground states of various quantum many-body systems, including complex frustrated magnets, demonstrating their potential in quantum physics research.

Contribution

It introduces neural network architectures capable of representing complex quantum ground states, including frustrated systems with sign problems, advancing the application of ANNs in quantum many-body physics.

Findings

ANNs can approximate ground states of free bosons and fermions.

Modified architectures succeed in learning complex sign rules in frustrated systems.

The method effectively explores ground states of the $J_1-J_2$ Heisenberg model.

Abstract

In this paper, we demonstrate the expressibility of artificial neural networks (ANNs) in quantum many-body physics by showing that a feed-forward neural network with a small number of hidden layers can be trained to approximate with high precision the ground states of some notable quantum many-body systems. We consider the one-dimensional free bosons and fermions, spinless fermions on a square lattice away from half-filling, as well as frustrated quantum magnetism with a rapidly oscillating ground-state characteristic function. In the latter case, an ANN with a standard architecture fails, while that with a slightly modified one successfully learns the frustration-induced complex sign rule in the ground state and approximates the ground states with high precisions. As an example of practical use of our method, we also perform the variational method to explore the ground state of an anti-ferromagnetic $J_1-J_2$ Heisenberg model.