A statistical mechanism for operator growth. (19th March 2021)

• Record Type: Journal Article
• Authors: Cao, Xiangyu
• Is Part Of: Journal of physics. Volume 54:Number 14(2021)
• Publication Date: 2021-03-19
• Subjects: quantum chaos -- quantum thermalization -- many-body localization -- spin models; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/abe77c
• Languages: English
• ISSNs: 1751-8113

Abstract

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 ⩾ 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 asymptotics 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.