Bounds on eigenstate thermalization
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915301947342848 |
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| author | Sugimoto, Shoki Hamazaki, Ryusuke Ueda, Masahito |
| author_facet | Sugimoto, Shoki Hamazaki, Ryusuke Ueda, Masahito |
| contents | The eigenstate thermalization hypothesis (ETH), which asserts that every eigenstate of a many-body quantum system is indistinguishable from a thermal ensemble, plays a pivotal role in understanding thermalization of isolated quantum systems. Yet, no evidence has been obtained as to whether the ETH holds for all few-body operators in a chaotic system; such few-body operators include key quantities in statistical mechanics, such as the total magnetization, the momentum distributions, and their low-order thermal and quantum fluctuations. Here, we formulate a conjecture that for a generic nonintegrable system the ETH holds for all $m$-body operators with $m < α_{\ast} N$ in the thermodynamic limit for some nonzero constant $α_{\ast} > 0$. We first prove this statement for systems with Haar-distributed energy eigenstates to analytically motivate our conjecture. We then verify the conjecture for generic spin, Bose, and Fermi systems with local and few-body interactions by large-scale numerical calculations. Our results imply that generic systems satisfy the ETH for all few-body operators, including their thermal and quantum fluctuations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10069 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bounds on eigenstate thermalization Sugimoto, Shoki Hamazaki, Ryusuke Ueda, Masahito Statistical Mechanics Quantum Physics The eigenstate thermalization hypothesis (ETH), which asserts that every eigenstate of a many-body quantum system is indistinguishable from a thermal ensemble, plays a pivotal role in understanding thermalization of isolated quantum systems. Yet, no evidence has been obtained as to whether the ETH holds for all few-body operators in a chaotic system; such few-body operators include key quantities in statistical mechanics, such as the total magnetization, the momentum distributions, and their low-order thermal and quantum fluctuations. Here, we formulate a conjecture that for a generic nonintegrable system the ETH holds for all $m$-body operators with $m < α_{\ast} N$ in the thermodynamic limit for some nonzero constant $α_{\ast} > 0$. We first prove this statement for systems with Haar-distributed energy eigenstates to analytically motivate our conjecture. We then verify the conjecture for generic spin, Bose, and Fermi systems with local and few-body interactions by large-scale numerical calculations. Our results imply that generic systems satisfy the ETH for all few-body operators, including their thermal and quantum fluctuations. |
| title | Bounds on eigenstate thermalization |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2303.10069 |