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Quantum Scrambling and State Dependence of the Butterfly Velocity

by Xizhi Han, Sean A. Hartnoll

Submission summary

As Contributors: Xizhi Han · Sean Hartnoll
Arxiv Link: https://arxiv.org/abs/1812.07598v2
Date submitted: 2019-03-27
Submitted by: Hartnoll, Sean
Submitted to: SciPost Physics
Domain(s): Theoretical
Subject area: Quantum Physics

Abstract

Operator growth in spatially local quantum many-body systems defines a scrambling velocity. We prove that this scrambling velocity bounds the state dependence (for example, the temperature dependence) of the out-of-time-ordered correlator in local lattice models. This amounts to a basic constraint on quantum chaos from locality. Thus, for example, while operators that do not grow with time can have an associated butterfly velocity, that velocity is necessarily temperature-independent. For scrambling operators, in contrast, the butterfly velocity shows a crossover from a microscopic high temperature value to a distinct value at temperatures below the energy gap.

Current status:
Editor-in-charge assigned

Submission & Refereeing History

Submission 1812.07598v2 on 27 March 2019

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