Hilbert subspace ergodicity

IF 3.7 2区物理与天体物理 Q1 Physics and Astronomy

Physical Review B Pub Date : 2025-04-18 DOI:10.1103/physrevb.111.144310

Leonard Logarić, John Goold, Shane Dooley

{"title":"Hilbert subspace ergodicity","authors":"Leonard Logarić, John Goold, Shane Dooley","doi":"10.1103/physrevb.111.144310","DOIUrl":null,"url":null,"abstract":"Ergodicity has been one of the fundamental concepts underpinning our understanding of thermalization in isolated systems since the first developments in classical statistical mechanics. Recently, a similar notion has been introduced for quantum systems, termed complete Hilbert space ergodicity (CHSE), in which the evolving quantum state explores all of the available Hilbert space. This contrasts with the eigenstate thermalization hypothesis (ETH), in which thermalization is formulated via the properties of matrix elements of local operators in the energy eigenbasis. In this work we explore how ETH-violation mechanisms, including quantum many-body scars and Hilbert space fragmentation, can affect complete Hilbert space ergodicity. We find that the presence of these mechanisms leads to CHSE in decoupled subspaces, a phenomenon we call Hilbert subspace ergodicity, and which represents a protocol for constructing t</a:mi></a:math>-designs in subspaces. Published by the American Physical Society 2025 ","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"88 1","pages":""},"PeriodicalIF":3.7000,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.111.144310","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}

引用次数: 0

Abstract

Ergodicity has been one of the fundamental concepts underpinning our understanding of thermalization in isolated systems since the first developments in classical statistical mechanics. Recently, a similar notion has been introduced for quantum systems, termed complete Hilbert space ergodicity (CHSE), in which the evolving quantum state explores all of the available Hilbert space. This contrasts with the eigenstate thermalization hypothesis (ETH), in which thermalization is formulated via the properties of matrix elements of local operators in the energy eigenbasis. In this work we explore how ETH-violation mechanisms, including quantum many-body scars and Hilbert space fragmentation, can affect complete Hilbert space ergodicity. We find that the presence of these mechanisms leads to CHSE in decoupled subspaces, a phenomenon we call Hilbert subspace ergodicity, and which represents a protocol for constructing t-designs in subspaces.

Published by the American Physical Society

2025

查看原文本刊更多论文

希尔伯特子空间遍历性

自经典统计力学的首次发展以来，遍历性一直是支撑我们理解孤立系统热化的基本概念之一。最近，在量子系统中引入了一个类似的概念，称为完全希尔伯特空间遍历性（CHSE），其中演化的量子态探索所有可用的希尔伯特空间。这与本征态热化假说（ETH）相反，在ETH中，热化是通过能量本征基中局部算符的矩阵元素的性质来表示的。在这项工作中，我们探讨了eth违反机制，包括量子多体伤痕和希尔伯特空间碎片，如何影响完全希尔伯特空间遍历性。我们发现这些机制的存在导致解耦子空间中的CHSE，这种现象我们称之为希尔伯特子空间遍历性，它代表了在子空间中构造t设计的协议。2025年由美国物理学会出版

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Physical Review B 物理-物理：凝聚态物理

CiteScore

6.70

自引率

32.40%

发文量

审稿时长

3.0 months

期刊介绍： Physical Review B (PRB) is the world’s largest dedicated physics journal, publishing approximately 100 new, high-quality papers each week. The most highly cited journal in condensed matter physics, PRB provides outstanding depth and breadth of coverage, combined with unrivaled context and background for ongoing research by scientists worldwide. PRB covers the full range of condensed matter, materials physics, and related subfields, including: -Structure and phase transitions -Ferroelectrics and multiferroics -Disordered systems and alloys -Magnetism -Superconductivity -Electronic structure, photonics, and metamaterials -Semiconductors and mesoscopic systems -Surfaces, nanoscience, and two-dimensional materials -Topological states of matter