Rényi entanglement entropy of spin chain with Generative Neural Networks

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.