Lee-Yang theory of quantum phase transitions with neural network quantum states

TL;DR

This paper introduces a method combining neural network quantum states with Lee-Yang theory to accurately predict quantum phase transition points in complex many-body systems across various lattice geometries.

Contribution

The authors develop a novel approach that integrates neural network quantum states with Lee-Yang theory to identify critical points in quantum phase transitions.

Findings

Accurately predicts critical fields in transverse-field Ising models

Consistent with large-scale quantum many-body methods

Applicable to complex systems like frustrated Heisenberg and Hubbard models

Abstract

Predicting the phase diagram of interacting quantum many-body systems is a central problem in condensed matter physics and related fields. A variety of quantum many-body systems, ranging from unconventional superconductors to spin liquids, exhibit complex competing phases whose theoretical description has been the focus of intense efforts. Here, we show that neural network quantum states can be combined with a Lee-Yang theory of quantum phase transitions to predict the critical points of strongly-correlated spin lattices. Specifically, we implement our approach for quantum phase transitions in the transverse-field Ising model on different lattice geometries in one, two, and three dimensions. We show that the Lee-Yang theory combined with neural network quantum states yields predictions of the critical field, which are consistent with large-scale quantum many-body methods. As such, our results provide a starting point for determining the phase diagram of more complex quantum many-body systems, including frustrated Heisenberg and Hubbard models.