R\'enyi entanglement entropy of spin chain with Generative Neural Networks

TL;DR

This paper introduces a neural network-based method to estimate Renyi entanglement entropy in spin systems, demonstrating its effectiveness on a quantum Ising chain with up to 32 spins.

Contribution

It presents a novel approach combining the replica trick with generative neural networks to estimate entanglement entropy in spin systems.

Findings

Successfully estimated second Renyi entropy for up to 32 spins.

Results agree with existing numerical and literature data.

Method can be extended to other spin systems and lattice field theories.

Abstract

We describe a method to estimate R\'enyi entanglement entropy of a spin system, which is based on the replica trick and generative neural networks with explicit probability estimation. It can be extended to any spin system or lattice field theory. We demonstrate our method on a one-dimensional quantum Ising spin chain. As the generative model, we use a hierarchy of autoregressive networks, allowing us to simulate up to 32 spins. We calculate the second R\'enyi entropy and its derivative and cross-check our results with the numerical evaluation of entropy and results available in the literature.