标题： 自旋链的Rényi纠缠熵与生成神经网络 显示英文标题

标题： Rényi entanglement entropy of spin chain with Generative Neural Networks

摘要： 我们描述了一种估计自旋系统Rényi纠缠熵的方法，该方法基于复制技巧和具有显式概率估计的生成神经网络。它可以扩展到任何自旋系统或格点场论。我们在一维量子伊辛自旋链上展示了我们的方法。作为生成模型，我们使用了自回归网络的层次结构，使我们能够模拟最多32个自旋。我们计算了第二Rényi熵及其导数，并通过熵的数值评估和文献中已有的结果对我们的结果进行了交叉验证。 显示英文摘要

摘要： 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.