Kai-Xin Hu , Yu Yan , Zhi-Xu Zhang , Shutian Liu , Wen-Xue Cui , Ji Cao , Shou Zhang , Hong-Fu Wang
{"title":"非互易耦合的d类拓扑系统中的反常相变","authors":"Kai-Xin Hu , Yu Yan , Zhi-Xu Zhang , Shutian Liu , Wen-Xue Cui , Ji Cao , Shou Zhang , Hong-Fu Wang","doi":"10.1016/j.cjph.2025.09.003","DOIUrl":null,"url":null,"abstract":"<div><div>We investigate class-D topological systems with nonreciprocal couplings and demonstrate their ability to host anomalous phase transitions. Specifically, we precisely determine the topological phase, characterized by the Chern number and bulk polarization, using the Green’s function and Wilson loop approaches. We rigorously confirm the validity of the anomalous transition lines by observing a remarkable consistency between the analytical zero-energy conditions and numerical phase transition boundaries. Meanwhile, bound states are present at the anomalous transition lines, but absent at the normal transition lines. Moreover, these bound states are localized at the system boundaries and are robust to disorders. Our work demonstrates that the anomalous transition lines in class-D Hermitian systems with nonreciprocal couplings exhibit richer physical phenomena than the normal transition lines, advancing the understanding of topological phase transitions.</div></div>","PeriodicalId":10340,"journal":{"name":"Chinese Journal of Physics","volume":"98 ","pages":"Pages 191-202"},"PeriodicalIF":4.6000,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Anomalous phase transitions in class-D topological systems with nonreciprocal couplings\",\"authors\":\"Kai-Xin Hu , Yu Yan , Zhi-Xu Zhang , Shutian Liu , Wen-Xue Cui , Ji Cao , Shou Zhang , Hong-Fu Wang\",\"doi\":\"10.1016/j.cjph.2025.09.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We investigate class-D topological systems with nonreciprocal couplings and demonstrate their ability to host anomalous phase transitions. Specifically, we precisely determine the topological phase, characterized by the Chern number and bulk polarization, using the Green’s function and Wilson loop approaches. We rigorously confirm the validity of the anomalous transition lines by observing a remarkable consistency between the analytical zero-energy conditions and numerical phase transition boundaries. Meanwhile, bound states are present at the anomalous transition lines, but absent at the normal transition lines. Moreover, these bound states are localized at the system boundaries and are robust to disorders. Our work demonstrates that the anomalous transition lines in class-D Hermitian systems with nonreciprocal couplings exhibit richer physical phenomena than the normal transition lines, advancing the understanding of topological phase transitions.</div></div>\",\"PeriodicalId\":10340,\"journal\":{\"name\":\"Chinese Journal of Physics\",\"volume\":\"98 \",\"pages\":\"Pages 191-202\"},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2025-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chinese Journal of Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0577907325003545\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chinese Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0577907325003545","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Anomalous phase transitions in class-D topological systems with nonreciprocal couplings
We investigate class-D topological systems with nonreciprocal couplings and demonstrate their ability to host anomalous phase transitions. Specifically, we precisely determine the topological phase, characterized by the Chern number and bulk polarization, using the Green’s function and Wilson loop approaches. We rigorously confirm the validity of the anomalous transition lines by observing a remarkable consistency between the analytical zero-energy conditions and numerical phase transition boundaries. Meanwhile, bound states are present at the anomalous transition lines, but absent at the normal transition lines. Moreover, these bound states are localized at the system boundaries and are robust to disorders. Our work demonstrates that the anomalous transition lines in class-D Hermitian systems with nonreciprocal couplings exhibit richer physical phenomena than the normal transition lines, advancing the understanding of topological phase transitions.
期刊介绍:
The Chinese Journal of Physics publishes important advances in various branches in physics, including statistical and biophysical physics, condensed matter physics, atomic/molecular physics, optics, particle physics and nuclear physics.
The editors welcome manuscripts on:
-General Physics: Statistical and Quantum Mechanics, etc.-
Gravitation and Astrophysics-
Elementary Particles and Fields-
Nuclear Physics-
Atomic, Molecular, and Optical Physics-
Quantum Information and Quantum Computation-
Fluid Dynamics, Nonlinear Dynamics, Chaos, and Complex Networks-
Plasma and Beam Physics-
Condensed Matter: Structure, etc.-
Condensed Matter: Electronic Properties, etc.-
Polymer, Soft Matter, Biological, and Interdisciplinary Physics.
CJP publishes regular research papers, feature articles and review papers.