具有生成神经网络的自旋链的雷尼纠缠熵。

IF 2.2 3区物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS

Physical Review E Pub Date : 2024-10-01 DOI:10.1103/PhysRevE.110.044116

Piotr Białas, Piotr Korcyl, Tomasz Stebel, Dawid Zapolski

{"title":"具有生成神经网络的自旋链的雷尼纠缠熵。","authors":"Piotr Białas, Piotr Korcyl, Tomasz Stebel, Dawid Zapolski","doi":"10.1103/PhysRevE.110.044116","DOIUrl":null,"url":null,"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.","PeriodicalId":48698,"journal":{"name":"Physical Review E","volume":"110 4-1","pages":"044116"},"PeriodicalIF":2.2000,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rényi entanglement entropy of a spin chain with generative neural networks.\",\"authors\":\"Piotr Białas, Piotr Korcyl, Tomasz Stebel, Dawid Zapolski\",\"doi\":\"10.1103/PhysRevE.110.044116\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":48698,\"journal\":{\"name\":\"Physical Review E\",\"volume\":\"110 4-1\",\"pages\":\"044116\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review E\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/PhysRevE.110.044116\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, FLUIDS & PLASMAS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review E","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/PhysRevE.110.044116","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, FLUIDS & PLASMAS","Score":null,"Total":0}

引用次数: 0

摘要

我们描述了一种估算自旋系统雷尼纠缠熵的方法，它基于复制技巧和显式概率估算的生成神经网络。它可以扩展到任何自旋系统或晶格场论。我们在一维量子伊辛自旋链上演示了我们的方法。作为生成模型，我们使用了自回归网络的层次结构，从而可以模拟多达 32 个自旋。我们计算了第二雷尼熵及其导数，并将我们的结果与熵的数值评估和文献中的结果进行了交叉检验。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Rényi entanglement entropy of a spin chain with generative neural networks.

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Physical Review E PHYSICS, FLUIDS & PLASMASPHYSICS, MATHEMAT-PHYSICS, MATHEMATICAL

CiteScore

4.50

自引率

16.70%

发文量

2110

期刊介绍： Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.