Machine learning quantum phases of matter beyond the fermion sign problem

TL;DR

This paper demonstrates that convolutional neural networks can identify quantum phase transitions in many-fermion systems using Green's functions from quantum Monte Carlo simulations, even in cases with a severe fermion sign problem.

Contribution

It introduces a machine learning approach that leverages Green's functions to detect quantum phases, bypassing the fermion sign problem in quantum Monte Carlo simulations.

Findings

CNN accurately identifies quantum phase transitions.

Green's function contains sufficient information for phase classification.

Method works despite severe fermion sign problem.

Abstract

State-of-the-art machine learning techniques promise to become a powerful tool in statistical mechanics via their capacity to distinguish different phases of matter in an automated way. Here we demonstrate that convolutional neural networks (CNN) can be optimized for quantum many-fermion systems such that they correctly identify and locate quantum phase transitions in such systems. Using auxiliary-field quantum Monte Carlo (QMC) simulations to sample the many-fermion system, we show that the Green's function (but not the auxiliary field) holds sufficient information to allow for the distinction of different fermionic phases via a CNN. We demonstrate that this QMC + machine learning approach works even for systems exhibiting a severe fermion sign problem where conventional approaches to extract information from the Green's function, e.g.~in the form of equal-time correlation functions, fail. We expect that this capacity of hierarchical machine learning techniques to circumvent the fermion sign problem will drive novel insights into some of the most fundamental problems in statistical physics.