{"title":"Non-Abelian permutations meet D4 group in a four-state non-Hermitian system","authors":"Linsheng Bao, Aoqian Shi, Yuchen Peng, Peng Peng, Jiayun Ning, Zhennan Wang, Chao Peng, Jianjun Liu","doi":"10.1103/physrevb.110.l020104","DOIUrl":null,"url":null,"abstract":"Encircling non-Hermitian exceptional points (EPs) leads to the swapping of eigenstates, which naturally corresponds to the different state permutations. Here, we find that non-Abelian permutations meet the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>D</mi><mn>4</mn></msub></math> group in a four-state non-Hermitian system. By encircling three different exceptional arcs within a three-dimensional parameter space, we present seven eigenvalue permutations and correlate them with seven nontrivial operations in the non-Abelian <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>D</mi><mn>4</mn></msub></math> group. Furthermore, our theory reveals the topological properties of higher-order EPs, improves the understanding of EPs in non-Hermitian systems, and offers a robust methodology for examining non-Abelian properties in systems with multiple EPs.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-07-29","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.110.l020104","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
Encircling non-Hermitian exceptional points (EPs) leads to the swapping of eigenstates, which naturally corresponds to the different state permutations. Here, we find that non-Abelian permutations meet the group in a four-state non-Hermitian system. By encircling three different exceptional arcs within a three-dimensional parameter space, we present seven eigenvalue permutations and correlate them with seven nontrivial operations in the non-Abelian group. Furthermore, our theory reveals the topological properties of higher-order EPs, improves the understanding of EPs in non-Hermitian systems, and offers a robust methodology for examining non-Abelian properties in systems with multiple EPs.
环绕非ermitian 特殊点(EPs)会导致特征状态的交换,这自然对应于不同的状态排列。在这里,我们发现非阿贝尔排列组合符合四态非ermitian 系统中的 D4 组。通过在三维参数空间中环绕三条不同的特殊弧线,我们提出了七种特征值排列,并将它们与非阿贝尔 D4 群中的七种非琐运算联系起来。此外,我们的理论揭示了高阶 EP 的拓扑特性,增进了对非ermitian 系统中 EP 的理解,并为研究具有多个 EP 的系统中的非阿贝尔特性提供了一种稳健的方法。
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