Topological Phases with Average Symmetries: The Decohered, the Disordered, and the Intrinsic
Global symmetries greatly enrich the landscape of topological quantum phases, playing an essential role from topological insulators to fractional quantum Hall effect. Topological phases in mixed quantum states, originating from decoherence in open quantum systems or disorders in imperfect crystallin...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-05-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.15.021062 |
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| author | Ruochen Ma Jian-Hao Zhang Zhen Bi Meng Cheng Chong Wang |
| author_facet | Ruochen Ma Jian-Hao Zhang Zhen Bi Meng Cheng Chong Wang |
| author_sort | Ruochen Ma |
| collection | DOAJ |
| description | Global symmetries greatly enrich the landscape of topological quantum phases, playing an essential role from topological insulators to fractional quantum Hall effect. Topological phases in mixed quantum states, originating from decoherence in open quantum systems or disorders in imperfect crystalline solids, have recently garnered significant interest. Unlike pure states, mixed quantum states can exhibit average symmetries—symmetries that keep the total ensemble invariant but not on each individual state. In this work, we present a systematic classification and characterization of average symmetry-protected topological (ASPT) phases applicable to generic symmetry groups, encompassing both average and exact symmetries, for bosonic and fermionic systems. Moreover, we formulate the theory of average symmetry-enriched topological (ASET) orders in disordered bosonic systems. Our systematic approach helps clarify nuanced issues in previous literature and uncovers compelling new physics. Notably, we discover that (1) the definition and classification of ASPT phases in decohered and disordered systems exhibit subtle differences, (2) despite these differences, ASPT phases in both settings can be classified and characterized under a unified framework of defect decoration and spectral sequence, (3) this systematic classification uncovers a plethora of ASPT phases that are intrinsically mixed, implying they can exclusively manifest in decohered or disordered systems where part of the symmetry is average, and (4) similarly for ASET, we find intrinsically disordered phases exhibiting exotic anyon behaviors—the ground states of such phases necessarily contain localized anyons, with gapless (yet still localized) excitation blue spectra. |
| format | Article |
| id | doaj-art-bb31b0e42e7e45b29c4f7faa61ec0e32 |
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| issn | 2160-3308 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | American Physical Society |
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| series | Physical Review X |
| spelling | doaj-art-bb31b0e42e7e45b29c4f7faa61ec0e322025-08-20T01:52:41ZengAmerican Physical SocietyPhysical Review X2160-33082025-05-0115202106210.1103/PhysRevX.15.021062Topological Phases with Average Symmetries: The Decohered, the Disordered, and the IntrinsicRuochen MaJian-Hao ZhangZhen BiMeng ChengChong WangGlobal symmetries greatly enrich the landscape of topological quantum phases, playing an essential role from topological insulators to fractional quantum Hall effect. Topological phases in mixed quantum states, originating from decoherence in open quantum systems or disorders in imperfect crystalline solids, have recently garnered significant interest. Unlike pure states, mixed quantum states can exhibit average symmetries—symmetries that keep the total ensemble invariant but not on each individual state. In this work, we present a systematic classification and characterization of average symmetry-protected topological (ASPT) phases applicable to generic symmetry groups, encompassing both average and exact symmetries, for bosonic and fermionic systems. Moreover, we formulate the theory of average symmetry-enriched topological (ASET) orders in disordered bosonic systems. Our systematic approach helps clarify nuanced issues in previous literature and uncovers compelling new physics. Notably, we discover that (1) the definition and classification of ASPT phases in decohered and disordered systems exhibit subtle differences, (2) despite these differences, ASPT phases in both settings can be classified and characterized under a unified framework of defect decoration and spectral sequence, (3) this systematic classification uncovers a plethora of ASPT phases that are intrinsically mixed, implying they can exclusively manifest in decohered or disordered systems where part of the symmetry is average, and (4) similarly for ASET, we find intrinsically disordered phases exhibiting exotic anyon behaviors—the ground states of such phases necessarily contain localized anyons, with gapless (yet still localized) excitation blue spectra.http://doi.org/10.1103/PhysRevX.15.021062 |
| spellingShingle | Ruochen Ma Jian-Hao Zhang Zhen Bi Meng Cheng Chong Wang Topological Phases with Average Symmetries: The Decohered, the Disordered, and the Intrinsic Physical Review X |
| title | Topological Phases with Average Symmetries: The Decohered, the Disordered, and the Intrinsic |
| title_full | Topological Phases with Average Symmetries: The Decohered, the Disordered, and the Intrinsic |
| title_fullStr | Topological Phases with Average Symmetries: The Decohered, the Disordered, and the Intrinsic |
| title_full_unstemmed | Topological Phases with Average Symmetries: The Decohered, the Disordered, and the Intrinsic |
| title_short | Topological Phases with Average Symmetries: The Decohered, the Disordered, and the Intrinsic |
| title_sort | topological phases with average symmetries the decohered the disordered and the intrinsic |
| url | http://doi.org/10.1103/PhysRevX.15.021062 |
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