Improved lattice method for determining entanglement measures in SU(N) gauge theories

TL;DR

This paper introduces an improved lattice method to accurately compute Rnyi entropies in SU(N) gauge theories, overcoming previous signal-to-noise challenges for high-precision entanglement measurements.

Contribution

The authors develop a novel approach that enhances the signal-to-noise ratio in lattice Monte Carlo calculations of entanglement measures in SU(N) gauge theories.

Findings

First results for SU(N) in 4 dimensions demonstrating the method's effectiveness.

Significant reduction in computational cost for high-precision Rnyi entropy calculations.

Potential for more detailed studies of entanglement in non-Abelian gauge theories.

Abstract

The determination of entanglement measures in SU(N) gauge theories is a non-trivial task. With the so-called "replica trick", a family of entanglement measures, known as "R\'enyi entropies", can be determined with lattice Monte Carlo. Unfortunately, the standard implementation of the replica method for SU(N) lattice gauge theories suffers from a severe signal-to-noise ratio problem, rendering high-precision studies of R\'enyi entropies prohibitively expensive. In this work, we propose a method to overcome the signal-to-noise ratio problem and show some first results for SU(N) in 4 dimensions.