Rényi entanglement entropy of spin chain with Generative Neural Networks

Abstract

We describe a method to estimate Rényi 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 Rényi entropy and its derivative and cross-check our results with the numerical evaluation of entropy and results available in the literature.

arXiv comment10 pages, 7 figures

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Cited by in corpus (4)

• Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems
• Flow-Based Sampling for Entanglement Entropy and the Machine Learning of Defects
• NeuMC -- a package for neural sampling for lattice field theories
• Hierarchical autoregressive neural networks in three-dimensional statistical system