发表机构
Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出扭曲熵序参量，利用辅助自由度记录拓扑缺陷信息，从约化密度矩阵中探测一维玻色子对称保护拓扑相，并推广至非普通群对称性。
AI 中文摘要
由F. Ares、S. Murciano和P. Calabrese引入的纠缠不对称性提供了一种基于密度矩阵的对称性破缺诊断工具，并成功捕捉了与破缺对称性模式相关的朗道数据。然而，目前已经公认，带隙量子多体系统可以表现出不仅由朗道对称性破缺所表征的相。一个基本的例子是对称保护拓扑（SPT）相，而纠缠不对称性的通常定义对此拓扑信息不敏感。在本工作中，我们引入了一个精细化的量，称为扭曲熵序参量，旨在从约化密度矩阵中探测SPT相，特别关注一维玻色子系统。我们构造的关键要素是一个辅助自由度，它相干地记录未扭曲态和与未破缺对称性的一端拓扑缺陷相关的扭曲态，从而使增广的密度矩阵保留缺陷端点所携带的电荷。我们在具体的晶格模型中演示了我们的提议，并将其进一步推广到普通群对称性之外，确立了其诊断SPT相的能力。这为建立用于诊断量子物质相的统一纠缠不对称性框架迈出了第一步。
英文摘要
Entanglement asymmetry, introduced by F. Ares, S. Murciano and P. Calabrese, provides a density-matrix diagnostic of symmetry breaking and successfully captures the Landau data associated with a broken symmetry pattern. However, it is by now well established that gapped quantum many-body systems can exhibit phases which are not characterized solely by Landau symmetry breaking. A fundamental example is a symmetry-protected topological (SPT) phase, and the ordinary definition of entanglement asymmetry is insensitive to this topological information. In this work we introduce a refined quantity, which we call the twisted entropic order parameter, designed to detect SPT phases from reduced density matrices, particularly focusing on one-dimensional bosonic systems. The key ingredient in our construction is an ancilla degrees of freedom that coherently records the untwisted state and the twisted state associated to a one-ended topological defect of unbroken symmetry, so that the enlarged density matrix retains the charge carried by the defect endpoint. We demonstrate our proposal in concrete lattice models and further generalize it beyond ordinary group symmetries, establishing its ability to diagnose SPT phases. This provides a first step toward a unified entanglement-asymmetry framework for diagnosing quantum phases of matter.
Comments42 pages, 4 figures
