Deep learning lattice gauge theories

TL;DR

This paper demonstrates that gauge-invariant neural network quantum states can accurately analyze $ ext{Z}_N$ lattice gauge theories, revealing phase transitions and critical behavior, offering a promising alternative to traditional Monte Carlo methods.

Contribution

It introduces a neural network approach for simulating lattice gauge theories, successfully identifying phase transitions and critical exponents in $ ext{Z}_N$ models in 2+1 dimensions.

Findings

Accurate ground state computations for $ ext{Z}_N$ lattice gauge theories.

Identification of continuous and weakly first-order phase transitions.

Agreement with known universality classes and critical exponents.

Abstract

Monte Carlo methods have led to profound insights into the strong-coupling behaviour of lattice gauge theories and produced remarkable results such as first-principles computations of hadron masses. Despite tremendous progress over the last four decades, fundamental challenges such as the sign problem and the inability to simulate real-time dynamics remain. Neural network quantum states have emerged as an alternative method that seeks to overcome these challenges. In this work, we use gauge-invariant neural network quantum states to accurately compute the ground state of $\mathbb{Z}_N$ lattice gauge theories in $2+1$ dimensions. Using transfer learning, we study the distinct topological phases and the confinement phase transition of these theories. For $\mathbb{Z}_2$, we identify a continuous transition and compute critical exponents, finding excellent agreement with existing numerics for the expected Ising universality class. In the $\mathbb{Z}_3$ case, we observe a weakly first-order transition and identify the critical coupling. Our findings suggest that neural network quantum states are a promising method for precise studies of lattice gauge theory.