Entanglement entropy from non-equilibrium lattice simulations

TL;DR

This paper introduces a Monte Carlo algorithm based on Jarzynski's equality to compute entanglement entropy in lattice models, successfully reproducing known results and exploring universal features in three dimensions.

Contribution

The paper presents a novel non-equilibrium Monte Carlo method for calculating entanglement entropy, extending its application to three-dimensional systems and extracting universal terms.

Findings

Successfully reproduces 2D Ising model entanglement entropy predictions

Extracts universal terms in 3D Ising model beyond the area law

Demonstrates the algorithm's potential for studying complex quantum systems

Abstract

Entanglement entropy encodes important features of strongly interacting quantum many-body systems and gauge theories, but its analytical study is still limited to systems with high level of symmetry. This motivates the search for efficient techniques to investigate this quantity numerically, through Monte Carlo calculations on the lattice. In this contribution, we discuss the computation of the entropic c-function by means of an algorithm based on Jarzynski's equality, which is an exact theorem from non equilibrium statistical mechanics. After presenting benchmark results for the Ising model in two dimensions, where our algorithm successfully reproduces the analytical predictions from conformal field theory, we discuss its generalization to the three-dimensional Ising model, for which we were able to extract universal terms beyond the area law. Finally we point out some future generalizations of this calculation.