Local Pairing of Feynman Histories in Many-Body Floquet Models

We study many-body quantum dynamics using Floquet quantum circuits in one space dimension as simple examples of systems with local interactions that support ergodic phases. Physical properties can be expressed in terms of multiple sums over Feynman histories, which for these models are paths or many...

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Autores principales:	S. J. Garratt, J. T. Chalker
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/da08b9ecbb6840779dfbd890c77794bd
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spelling	oai:doaj.org-article:da08b9ecbb6840779dfbd890c77794bd2021-12-02T17:58:58ZLocal Pairing of Feynman Histories in Many-Body Floquet Models10.1103/PhysRevX.11.0210512160-3308https://doaj.org/article/da08b9ecbb6840779dfbd890c77794bd2021-06-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.021051http://doi.org/10.1103/PhysRevX.11.021051https://doaj.org/toc/2160-3308We study many-body quantum dynamics using Floquet quantum circuits in one space dimension as simple examples of systems with local interactions that support ergodic phases. Physical properties can be expressed in terms of multiple sums over Feynman histories, which for these models are paths or many-body orbits in Fock space. A natural simplification of such sums is the diagonal approximation, where the only terms that are retained are ones in which each path is paired with a partner that carries the complex conjugate weight. We identify the regime in which the diagonal approximation holds and the nature of the leading corrections to it. We focus on the behavior of the spectral form factor (SFF) and of matrix elements of local operators, averaged over an ensemble of random circuits, making comparisons with the predictions of random matrix theory (RMT) and the eigenstate thermalization hypothesis (ETH). We show that properties are dominated at long times by contributions to orbit sums in which each orbit is paired locally with a conjugate, as in the diagonal approximation, but that in large systems these contributions consist of many spatial domains, with distinct local pairings in neighboring domains. The existence of these domains is reflected in deviations of the SFF from RMT predictions, and of matrix element correlations from ETH predictions; deviations of both kinds diverge with system size. We demonstrate that our physical picture of orbit-pairing domains has a precise correspondence in the spectral properties of a transfer matrix that acts in the space direction to generate the ensemble-averaged SFF. In addition, we find that domains of a second type control non-Gaussian fluctuations of the SFF. These domains are separated by walls that are related to the entanglement membrane, known to characterize the scrambling of quantum information.S. J. GarrattJ. T. ChalkerAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 2, p 021051 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 S. J. Garratt J. T. Chalker Local Pairing of Feynman Histories in Many-Body Floquet Models
description	We study many-body quantum dynamics using Floquet quantum circuits in one space dimension as simple examples of systems with local interactions that support ergodic phases. Physical properties can be expressed in terms of multiple sums over Feynman histories, which for these models are paths or many-body orbits in Fock space. A natural simplification of such sums is the diagonal approximation, where the only terms that are retained are ones in which each path is paired with a partner that carries the complex conjugate weight. We identify the regime in which the diagonal approximation holds and the nature of the leading corrections to it. We focus on the behavior of the spectral form factor (SFF) and of matrix elements of local operators, averaged over an ensemble of random circuits, making comparisons with the predictions of random matrix theory (RMT) and the eigenstate thermalization hypothesis (ETH). We show that properties are dominated at long times by contributions to orbit sums in which each orbit is paired locally with a conjugate, as in the diagonal approximation, but that in large systems these contributions consist of many spatial domains, with distinct local pairings in neighboring domains. The existence of these domains is reflected in deviations of the SFF from RMT predictions, and of matrix element correlations from ETH predictions; deviations of both kinds diverge with system size. We demonstrate that our physical picture of orbit-pairing domains has a precise correspondence in the spectral properties of a transfer matrix that acts in the space direction to generate the ensemble-averaged SFF. In addition, we find that domains of a second type control non-Gaussian fluctuations of the SFF. These domains are separated by walls that are related to the entanglement membrane, known to characterize the scrambling of quantum information.
format	article
author	S. J. Garratt J. T. Chalker
author_facet	S. J. Garratt J. T. Chalker
author_sort	S. J. Garratt
title	Local Pairing of Feynman Histories in Many-Body Floquet Models
title_short	Local Pairing of Feynman Histories in Many-Body Floquet Models
title_full	Local Pairing of Feynman Histories in Many-Body Floquet Models
title_fullStr	Local Pairing of Feynman Histories in Many-Body Floquet Models
title_full_unstemmed	Local Pairing of Feynman Histories in Many-Body Floquet Models
title_sort	local pairing of feynman histories in many-body floquet models
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/da08b9ecbb6840779dfbd890c77794bd
work_keys_str_mv	AT sjgarratt localpairingoffeynmanhistoriesinmanybodyfloquetmodels AT jtchalker localpairingoffeynmanhistoriesinmanybodyfloquetmodels
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Local Pairing of Feynman Histories in Many-Body Floquet Models

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