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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2021

A statistical mechanism for operator growth

Xiangyu Cao
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Résumé

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≥2d≥2d \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.

Dates et versions

hal-03170370 , version 1 (05-01-2021)
hal-03170370 , version 2 (16-03-2021)

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Citer

Xiangyu Cao. A statistical mechanism for operator growth. Journal of Physics A: Mathematical and Theoretical, 2021, 54 (14), pp.144001. ⟨10.1088/1751-8121/abe77c⟩. ⟨hal-03170370v2⟩
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