Normal weak eigenstate thermalization
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915280841605120 |
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| author | Łydżba, Patrycja Świętek, Rafał Mierzejewski, Marcin Rigol, Marcos Vidmar, Lev |
| author_facet | Łydżba, Patrycja Świętek, Rafał Mierzejewski, Marcin Rigol, Marcos Vidmar, Lev |
| contents | Eigenstate thermalization has been numerically shown to occur for few-body observables in a wide range of nonintegrable models. For intensive sums of few-body observables, a weaker version of eigenstate thermalization known as weak eigenstate thermalization has been proved to occur in general. Here, we unveil a stricter weak eigenstate thermalization phenomenon that occurs in quadratic models exhibiting quantum chaos in the single-particle sector (quantum-chaotic quadratic models) and in integrable interacting models. In such models, we argue that few-body observables that have a properly defined system-size independent norm are guaranteed to exhibit at least a polynomially vanishing variance (over the entire many-body energy spectrum) of the diagonal matrix elements, a phenomenon we dub normal weak eigenstate thermalization. We prove that normal weak eigenstate thermalization is a consequence of single-particle eigenstate thermalization, i.e., it can be viewed as a manifestation of quantum chaos at the single-particle level. We report numerical evidence of normal weak eigenstate thermalization for quantum-chaotic quadratic models such as the three-dimensional Anderson model in the delocalized regime and the power-law random banded matrix model, as well as for the integrable interacting spin-1/2 XYZ and XXZ models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02199 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normal weak eigenstate thermalization Łydżba, Patrycja Świętek, Rafał Mierzejewski, Marcin Rigol, Marcos Vidmar, Lev Statistical Mechanics Disordered Systems and Neural Networks Strongly Correlated Electrons Quantum Physics Eigenstate thermalization has been numerically shown to occur for few-body observables in a wide range of nonintegrable models. For intensive sums of few-body observables, a weaker version of eigenstate thermalization known as weak eigenstate thermalization has been proved to occur in general. Here, we unveil a stricter weak eigenstate thermalization phenomenon that occurs in quadratic models exhibiting quantum chaos in the single-particle sector (quantum-chaotic quadratic models) and in integrable interacting models. In such models, we argue that few-body observables that have a properly defined system-size independent norm are guaranteed to exhibit at least a polynomially vanishing variance (over the entire many-body energy spectrum) of the diagonal matrix elements, a phenomenon we dub normal weak eigenstate thermalization. We prove that normal weak eigenstate thermalization is a consequence of single-particle eigenstate thermalization, i.e., it can be viewed as a manifestation of quantum chaos at the single-particle level. We report numerical evidence of normal weak eigenstate thermalization for quantum-chaotic quadratic models such as the three-dimensional Anderson model in the delocalized regime and the power-law random banded matrix model, as well as for the integrable interacting spin-1/2 XYZ and XXZ models. |
| title | Normal weak eigenstate thermalization |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2404.02199 |