Bounds on eigenstate thermalization

• URL: http://arxiv.org/abs/2303.10069v2
• Date: Sun, 15 Dec 2024 06:04:38 GMT
• Title: Bounds on eigenstate thermalization
• Authors: Shoki Sugimoto, Ryusuke Hamazaki, Masahito Ueda,
• Abstract summary: The eigenstate thermalization hypothesis (ETH) asserts that every eigenstate of a many-body quantum system is indistinguishable from a thermal ensemble. Here, we show the existence of upper and lower bounds on $m_ast$ such that all $m$-body operators with $m m_ast$ satisfy the ETH. Our results imply that generic systems satisfy the ETH for any few-body operators, including their thermal and quantum fluctuations.
• Score: 8.329456268842227
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• Abstract: 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 any few-body operators in a chaotic system; such few-body operators include crucial quantities in statistical mechanics, such as the total magnetization, the momentum distribution, and their low-order thermal and quantum fluctuations. Here, we show the existence of upper and lower bounds on $m_{\ast}$ such that all $m$-body operators with $m < m_{\ast}$ satisfy the ETH. For $N$-particles systems, these bounds are given in the form ${\alpha}_L \leq m_{\ast} / N \leq {\alpha}_U$, where ${\alpha}_L$ and ${\alpha}_U$ are $N$-independent positive numbers. We rigorously prove this statement for systems with Haar-distributed energy eigenstates and provide numerical evidence for generic systems with local and few-body interactions. Our results imply that generic systems satisfy the ETH for any few-body operators, including their thermal and quantum fluctuations.

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