Entanglement Membrane in Chaotic Many-Body Systems

In certain analytically tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and other related dynamical observables reduces to an effective theory of an “entanglement membrane” in spacetime. These tractable systems inv...

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Autores principales:	Tianci Zhou, Adam Nahum
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/7ce24056182f4a13842422f1ee301136
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spelling	oai:doaj.org-article:7ce24056182f4a13842422f1ee3011362021-12-02T10:58:06ZEntanglement Membrane in Chaotic Many-Body Systems10.1103/PhysRevX.10.0310662160-3308https://doaj.org/article/7ce24056182f4a13842422f1ee3011362020-09-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.031066http://doi.org/10.1103/PhysRevX.10.031066https://doaj.org/toc/2160-3308In certain analytically tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and other related dynamical observables reduces to an effective theory of an “entanglement membrane” in spacetime. These tractable systems involve an average over random local unitaries defining the dynamical evolution. We show here how to make sense of this membrane in more realistic models, which do not involve an average over random unitaries. Our approach relies on introducing effective pairing degrees of freedom in spacetime, describing a pairing of forward and backward Feynman trajectories, inspired by the structure emerging in random unitary circuits. This viewpoint provides a framework for applying ideas of coarse graining to dynamical quantities in chaotic systems. We apply the approach to some translationally invariant Floquet spin chains studied in the literature. We show that a consistent line tension may be defined for the entanglement membrane and that there are qualitative differences in this tension between generic models and “dual-unitary” circuits. These results allow scaling pictures for out-of-time-order correlators and for entanglement to be taken over from random circuits to nonrandom Floquet models. We also provide an efficient numerical algorithm for determining the entanglement line tension in 1+1D.Tianci ZhouAdam NahumAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 3, p 031066 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Tianci Zhou Adam Nahum Entanglement Membrane in Chaotic Many-Body Systems
description	In certain analytically tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and other related dynamical observables reduces to an effective theory of an “entanglement membrane” in spacetime. These tractable systems involve an average over random local unitaries defining the dynamical evolution. We show here how to make sense of this membrane in more realistic models, which do not involve an average over random unitaries. Our approach relies on introducing effective pairing degrees of freedom in spacetime, describing a pairing of forward and backward Feynman trajectories, inspired by the structure emerging in random unitary circuits. This viewpoint provides a framework for applying ideas of coarse graining to dynamical quantities in chaotic systems. We apply the approach to some translationally invariant Floquet spin chains studied in the literature. We show that a consistent line tension may be defined for the entanglement membrane and that there are qualitative differences in this tension between generic models and “dual-unitary” circuits. These results allow scaling pictures for out-of-time-order correlators and for entanglement to be taken over from random circuits to nonrandom Floquet models. We also provide an efficient numerical algorithm for determining the entanglement line tension in 1+1D.
format	article
author	Tianci Zhou Adam Nahum
author_facet	Tianci Zhou Adam Nahum
author_sort	Tianci Zhou
title	Entanglement Membrane in Chaotic Many-Body Systems
title_short	Entanglement Membrane in Chaotic Many-Body Systems
title_full	Entanglement Membrane in Chaotic Many-Body Systems
title_fullStr	Entanglement Membrane in Chaotic Many-Body Systems
title_full_unstemmed	Entanglement Membrane in Chaotic Many-Body Systems
title_sort	entanglement membrane in chaotic many-body systems
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/7ce24056182f4a13842422f1ee301136
work_keys_str_mv	AT tiancizhou entanglementmembraneinchaoticmanybodysystems AT adamnahum entanglementmembraneinchaoticmanybodysystems
_version_	1718396407695540224

Entanglement Membrane in Chaotic Many-Body Systems

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