# Entanglement entropy from nonequilibrium work

## TL;DR

This paper introduces a novel fluctuation theorem-based method to estimate Rènyi entanglement entropy in quantum many-body systems, enabling efficient analysis of large-scale simulations and universal properties.

## Contribution

It develops a new framework linking nonequilibrium work fluctuation theorems to entanglement entropy estimation, improving computational efficiency and scalability.

## Key findings

- Efficient estimation of entanglement entropy using nonequilibrium work methods.
- Application to large-scale quantum Monte Carlo simulations of SU(N) spin models.
- Access to unprecedented system sizes up to 192 x 96 spins.

## Abstract

The R\'enyi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies. We introduce an external field $\lambda$ that controls the partition function topology, allowing us to define a notion of nonequilibrium work as $\lambda$ is varied smoothly. Nonequilibrium fluctuation theorems of the work provide us with statistically exact estimates of the R\'enyi entanglement entropy. This framework also naturally leads to the idea of using quench functions with spatially smooth profiles, providing us a way to average over lattice scale features of the entanglement entropy while preserving long distance universal information. We use these ideas to extract universal information from quantum Monte Carlo simulations of SU(N) spin models in one and two dimensions. The vast gain in efficiency of this method allows us to access unprecedented system sizes up to 192 x 96 spins for the square lattice Heisenberg antiferromagnet.