Subsystem eigenstate thermalization hypothesis for translation invariant systems
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911885380550656 |
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| author | Huang, Zhiqiang Guo, Xiao-Kan |
| author_facet | Huang, Zhiqiang Guo, Xiao-Kan |
| contents | The eigenstate thermalization hypothesis for translation invariant quantum spin systems has been proved recently by using random matrices. In this paper, we study the subsystem version of eigenstate thermalization hypothesis for translation invariant quantum systems without referring to random matrices. We first find a relation between the quantum variance and the Belavkin-Staszewski relative entropy. Then, by showing the small upper bounds on the quantum variance and the Belavkin-Staszewski relative entropy, we prove the subsystem eigenstate thermalization hypothesis for translation invariant quantum systems with an algebraic speed of convergence in an elementary way. The proof holds for most of the translation invariant quantum lattice models with exponential or algebraic decays of correlations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00410 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Subsystem eigenstate thermalization hypothesis for translation invariant systems Huang, Zhiqiang Guo, Xiao-Kan Quantum Physics Statistical Mechanics The eigenstate thermalization hypothesis for translation invariant quantum spin systems has been proved recently by using random matrices. In this paper, we study the subsystem version of eigenstate thermalization hypothesis for translation invariant quantum systems without referring to random matrices. We first find a relation between the quantum variance and the Belavkin-Staszewski relative entropy. Then, by showing the small upper bounds on the quantum variance and the Belavkin-Staszewski relative entropy, we prove the subsystem eigenstate thermalization hypothesis for translation invariant quantum systems with an algebraic speed of convergence in an elementary way. The proof holds for most of the translation invariant quantum lattice models with exponential or algebraic decays of correlations. |
| title | Subsystem eigenstate thermalization hypothesis for translation invariant systems |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2312.00410 |