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Condensed Matter > Statistical Mechanics
Title: General Eigenstate Thermalization via Free Cumulants in Quantum Lattice Systems
(Submitted on 1 Mar 2023 (v1), last revised 31 Jul 2023 (this version, v3))
Abstract: The Eigenstate-Thermalization-Hypothesis (ETH) has been established as the general framework to understand quantum statistical mechanics. Only recently has the attention been paid to so-called general ETH, which accounts for higher-order correlations among matrix elements, and that can be rationalized theoretically using the language of Free Probability. In this work, we perform the first numerical investigation of the general ETH in physical many-body systems with local interactions by testing the decomposition of higher-order correlators into free cumulants. We perform exact diagonalization on two classes of local non-integrable (chaotic) quantum many-body systems: spin chain Hamiltonians and Floquet brickwork unitary circuits. We show that the dynamics of four-time correlation functions are encoded in fourth-order free cumulants, as predicted by ETH. Their non-trivial frequency dependence encodes the physical properties of local many-body systems and distinguishes them from structureless, rotationally invariant ensembles of random matrices.
Submission history
From: Silvia Pappalardi [view email][v1] Wed, 1 Mar 2023 18:18:51 GMT (2816kb,D)
[v2] Tue, 4 Apr 2023 16:24:17 GMT (2816kb,D)
[v3] Mon, 31 Jul 2023 09:04:34 GMT (6739kb,D)
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