A statistical mechanism for operator growth
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.
- Publication:
-
Journal of Physics A Mathematical General
- Pub Date:
- April 2021
- DOI:
- 10.1088/1751-8121/abe77c
- arXiv:
- arXiv:2012.06544
- Bibcode:
- 2021JPhA...54n4001C
- Keywords:
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- quantum chaos;
- quantum thermalization;
- many-body localization;
- spin models;
- Condensed Matter - Statistical Mechanics;
- High Energy Physics - Theory;
- Quantum Physics
- E-Print:
- 9 pages, 0 figures