2023/03/17 by Shoki Sugimoto, Ryusuke Hamazaki, Sugimoto, Shoki +3 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2303.10069
openalex publication_date 2023/03/17 · openalex created_date 2023/03/21 · openalex updated_date 2026/07/28
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 simultaneously for all m-body operators with m < α∗ N in the thermodynamic limit for some nonzero constant α∗ > 0. We first show the existence of such nontrivial constants for idealized (pseudo) random-matrix descriptions of many-body eigenstates. 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 simultaneously for all few-body operators, including their thermal and quantum fluctuations.