Anomalies of average symmetries: entanglement and open quantum systems
Abstract Symmetries and their anomalies are powerful tools for understanding quantum systems. However, realistic systems are often subject to disorders, dissipation and decoherence. In many circumstances, symmetries are not exact but only on average. This work investigates the constraints on mixed s...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-10-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP10(2024)134 |
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| author | Po-Shen Hsin Zhu-Xi Luo Hao-Yu Sun |
| author_facet | Po-Shen Hsin Zhu-Xi Luo Hao-Yu Sun |
| author_sort | Po-Shen Hsin |
| collection | DOAJ |
| description | Abstract Symmetries and their anomalies are powerful tools for understanding quantum systems. However, realistic systems are often subject to disorders, dissipation and decoherence. In many circumstances, symmetries are not exact but only on average. This work investigates the constraints on mixed states resulting from non-commuting average symmetries. We will focus on the cases where the commutation relations of the average symmetry generators are violated by nontrivial phases, and call such average symmetry anomalous. We show that anomalous average symmetry implies degeneracy in the density matrix eigenvalues, and present several lattice examples with average symmetries, including XY chain, Heisenberg chain, and deformed toric code models. In certain cases, the results can be further extended to reduced density matrices, leading to a new lower bound on the entanglement entropy. We discuss several applications in the contexts of many body localization, quantum channels, entanglement phase transitions and also derive new constraints on the Lindbladian evolution of open quantum systems. |
| format | Article |
| id | doaj-art-937e7a14f3ba4ef9b4af6b3be4b80a59 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-937e7a14f3ba4ef9b4af6b3be4b80a592024-12-08T12:11:14ZengSpringerOpenJournal of High Energy Physics1029-84792024-10-0120241014210.1007/JHEP10(2024)134Anomalies of average symmetries: entanglement and open quantum systemsPo-Shen Hsin0Zhu-Xi Luo1Hao-Yu Sun2Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California Los AngelesDepartment of Physics, Harvard UniversityWeinberg Institute, Department of Physics, The University of Texas at AustinAbstract Symmetries and their anomalies are powerful tools for understanding quantum systems. However, realistic systems are often subject to disorders, dissipation and decoherence. In many circumstances, symmetries are not exact but only on average. This work investigates the constraints on mixed states resulting from non-commuting average symmetries. We will focus on the cases where the commutation relations of the average symmetry generators are violated by nontrivial phases, and call such average symmetry anomalous. We show that anomalous average symmetry implies degeneracy in the density matrix eigenvalues, and present several lattice examples with average symmetries, including XY chain, Heisenberg chain, and deformed toric code models. In certain cases, the results can be further extended to reduced density matrices, leading to a new lower bound on the entanglement entropy. We discuss several applications in the contexts of many body localization, quantum channels, entanglement phase transitions and also derive new constraints on the Lindbladian evolution of open quantum systems.https://doi.org/10.1007/JHEP10(2024)134Global SymmetriesTopological States of MatterWilson’t Hooft and Polyakov loopsDiscrete Symmetries |
| spellingShingle | Po-Shen Hsin Zhu-Xi Luo Hao-Yu Sun Anomalies of average symmetries: entanglement and open quantum systems Journal of High Energy Physics Global Symmetries Topological States of Matter Wilson ’t Hooft and Polyakov loops Discrete Symmetries |
| title | Anomalies of average symmetries: entanglement and open quantum systems |
| title_full | Anomalies of average symmetries: entanglement and open quantum systems |
| title_fullStr | Anomalies of average symmetries: entanglement and open quantum systems |
| title_full_unstemmed | Anomalies of average symmetries: entanglement and open quantum systems |
| title_short | Anomalies of average symmetries: entanglement and open quantum systems |
| title_sort | anomalies of average symmetries entanglement and open quantum systems |
| topic | Global Symmetries Topological States of Matter Wilson ’t Hooft and Polyakov loops Discrete Symmetries |
| url | https://doi.org/10.1007/JHEP10(2024)134 |
| work_keys_str_mv | AT poshenhsin anomaliesofaveragesymmetriesentanglementandopenquantumsystems AT zhuxiluo anomaliesofaveragesymmetriesentanglementandopenquantumsystems AT haoyusun anomaliesofaveragesymmetriesentanglementandopenquantumsystems |