Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects

TL;DR

This paper presents a new flow-based generative modeling approach combined with the replica trick to efficiently compute Re9nyi entanglement entropies in lattice quantum field theories, outperforming traditional Monte Carlo methods.

Contribution

It introduces a novel neural network architecture that leverages flow-based models and lattice defects to improve entanglement entropy calculations in quantum field theories.

Findings

Outperforms state-of-the-art Monte Carlo calculations

Demonstrates promising scaling with defect size

Effective in b4^4 scalar field theory in 2D and 3D

Abstract

We introduce a novel technique to numerically calculate R\'enyi entanglement entropies in lattice quantum field theory using generative models. We describe how flow-based approaches can be combined with the replica trick using a custom neural-network architecture around a lattice defect connecting two replicas. Numerical tests for the $\phi^4$ scalar field theory in two and three dimensions demonstrate that our technique outperforms state-of-the-art Monte Carlo calculations, and exhibit a promising scaling with the defect size.