Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems
The generalized Gibbs ensemble (GGE), which involves multiple conserved quantities other than the Hamiltonian, has served as the statistical-mechanical description of the long-time behavior for several isolated integrable quantum systems. We argue that the GGE may involve a noncommutative set of con...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-09-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.033403 |
| _version_ | 1797211308731400192 |
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| author | Kouhei Fukai Yuji Nozawa Koji Kawahara Tatsuhiko N. Ikeda |
| author_facet | Kouhei Fukai Yuji Nozawa Koji Kawahara Tatsuhiko N. Ikeda |
| author_sort | Kouhei Fukai |
| collection | DOAJ |
| description | The generalized Gibbs ensemble (GGE), which involves multiple conserved quantities other than the Hamiltonian, has served as the statistical-mechanical description of the long-time behavior for several isolated integrable quantum systems. We argue that the GGE may involve a noncommutative set of conserved quantities in view of the maximum entropy principle and show that the GGE thus generalized (noncommutative GGE, NCGGE) gives a more qualitatively accurate description of the long-time behaviors than that of the conventional GGE. Providing a clear understanding of why the (NC)GGE well describes the long-time behaviors, we construct, for noninteracting models, the exact NCGGE that describes the long-time behaviors without an error even at finite system size. It is noteworthy that the NCGGE involves nonlocal conserved quantities, which can be necessary for describing long-time behaviors of local observables. We also give some extensions of the NCGGE and demonstrate how accurately they describe the long-time behaviors of few-body observables. |
| first_indexed | 2024-04-24T10:24:26Z |
| format | Article |
| id | doaj.art-ff3841d40e3f4be19256a8344711be5a |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:24:26Z |
| publishDate | 2020-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-ff3841d40e3f4be19256a8344711be5a2024-04-12T17:00:31ZengAmerican Physical SocietyPhysical Review Research2643-15642020-09-012303340310.1103/PhysRevResearch.2.033403Noncommutative generalized Gibbs ensemble in isolated integrable quantum systemsKouhei FukaiYuji NozawaKoji KawaharaTatsuhiko N. IkedaThe generalized Gibbs ensemble (GGE), which involves multiple conserved quantities other than the Hamiltonian, has served as the statistical-mechanical description of the long-time behavior for several isolated integrable quantum systems. We argue that the GGE may involve a noncommutative set of conserved quantities in view of the maximum entropy principle and show that the GGE thus generalized (noncommutative GGE, NCGGE) gives a more qualitatively accurate description of the long-time behaviors than that of the conventional GGE. Providing a clear understanding of why the (NC)GGE well describes the long-time behaviors, we construct, for noninteracting models, the exact NCGGE that describes the long-time behaviors without an error even at finite system size. It is noteworthy that the NCGGE involves nonlocal conserved quantities, which can be necessary for describing long-time behaviors of local observables. We also give some extensions of the NCGGE and demonstrate how accurately they describe the long-time behaviors of few-body observables.http://doi.org/10.1103/PhysRevResearch.2.033403 |
| spellingShingle | Kouhei Fukai Yuji Nozawa Koji Kawahara Tatsuhiko N. Ikeda Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems Physical Review Research |
| title | Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems |
| title_full | Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems |
| title_fullStr | Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems |
| title_full_unstemmed | Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems |
| title_short | Noncommutative generalized Gibbs ensemble in isolated integrable quantum systems |
| title_sort | noncommutative generalized gibbs ensemble in isolated integrable quantum systems |
| url | http://doi.org/10.1103/PhysRevResearch.2.033403 |
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