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Condensed Matter > Statistical Mechanics
Title: A statistical mechanism for operator growth
(Submitted on 11 Dec 2020 (v1), last revised 10 Jun 2021 (this version, v2))
Abstract: It was recently conjectured that in generic quantum many-body systems, the spectral density of local operators has the slowest high-frequency decay as permitted by locality. We show that the infinite-temperature version of this "universal operator growth hypothesis" holds for the quantum Ising spin model in $d \ge 2$ dimensions, and for the chaotic Ising chain (with longitudinal and transverse fields) in one dimension. Moreover, the disordered chaotic Ising chain that exhibits many-body localization can have the same high-frequency spectral density decay as thermalizing models. Our argument is statistical in nature, and is based on the observation that the moments of the spectral density can be written as a sign-problem-free sum over paths of Pauli string operators.
Submission history
From: Xiangyu Cao [view email][v1] Fri, 11 Dec 2020 18:17:34 GMT (25kb)
[v2] Thu, 10 Jun 2021 09:26:57 GMT (25kb)
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