Influence Matrix Approach to Many-Body Floquet Dynamics

Recent experimental and theoretical works have made much progress toward understanding nonequilibrium phenomena in thermalizing systems, which act as thermal baths for their small subsystems, and many-body localized systems, which fail to do so. The description of time evolution in many-body systems...

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Autores principales:	Alessio Lerose, Michael Sonner, Dmitry A. Abanin
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/b354174a64d84de1978bfb910325e0a8
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spelling	oai:doaj.org-article:b354174a64d84de1978bfb910325e0a82021-12-02T14:45:34ZInfluence Matrix Approach to Many-Body Floquet Dynamics10.1103/PhysRevX.11.0210402160-3308https://doaj.org/article/b354174a64d84de1978bfb910325e0a82021-05-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.021040http://doi.org/10.1103/PhysRevX.11.021040https://doaj.org/toc/2160-3308Recent experimental and theoretical works have made much progress toward understanding nonequilibrium phenomena in thermalizing systems, which act as thermal baths for their small subsystems, and many-body localized systems, which fail to do so. The description of time evolution in many-body systems is generally challenging due to the dynamical generation of quantum entanglement. In this work, we introduce an approach to study quantum many-body dynamics, inspired by the Feynman-Vernon influence functional. Focusing on a family of interacting, Floquet spin chains, we consider a Keldysh path-integral description of the dynamics. The central object in our approach is the influence matrix, which describes the effect of the system on the dynamics of a local subsystem. For translationally invariant models, we formulate a self-consistency equation for the influence matrix. For certain special values of the model parameters, we obtain an exact solution which represents a perfect dephaser (PD). Physically, a PD corresponds to a many-body system that acts as a perfectly Markovian bath on itself: at each period, it measures every spin. For the models considered here, we establish that PD points include dual-unitary circuits investigated in recent works. In the vicinity of PD points, the system is not perfectly Markovian, but rather acts as a bath with a short memory time. In this case, we demonstrate that the self-consistency equation can be solved using matrix-product states (MPS) methods, as the influence matrix temporal entanglement is low. A combination of analytical insights and MPS computations allows us to characterize the structure of the influence matrix in terms of an effective “statistical-mechanics” description. We finally illustrate the predictive power of this description by analytically computing how quickly an embedded impurity spin thermalizes. The influence matrix approach formulated here provides an intuitive view of the quantum many-body dynamics problem, opening a path to constructing models of thermalizing dynamics that are solvable or can be efficiently treated by MPS-based methods and to further characterizing quantum ergodicity or lack thereof.Alessio LeroseMichael SonnerDmitry A. AbaninAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 2, p 021040 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Alessio Lerose Michael Sonner Dmitry A. Abanin Influence Matrix Approach to Many-Body Floquet Dynamics
description	Recent experimental and theoretical works have made much progress toward understanding nonequilibrium phenomena in thermalizing systems, which act as thermal baths for their small subsystems, and many-body localized systems, which fail to do so. The description of time evolution in many-body systems is generally challenging due to the dynamical generation of quantum entanglement. In this work, we introduce an approach to study quantum many-body dynamics, inspired by the Feynman-Vernon influence functional. Focusing on a family of interacting, Floquet spin chains, we consider a Keldysh path-integral description of the dynamics. The central object in our approach is the influence matrix, which describes the effect of the system on the dynamics of a local subsystem. For translationally invariant models, we formulate a self-consistency equation for the influence matrix. For certain special values of the model parameters, we obtain an exact solution which represents a perfect dephaser (PD). Physically, a PD corresponds to a many-body system that acts as a perfectly Markovian bath on itself: at each period, it measures every spin. For the models considered here, we establish that PD points include dual-unitary circuits investigated in recent works. In the vicinity of PD points, the system is not perfectly Markovian, but rather acts as a bath with a short memory time. In this case, we demonstrate that the self-consistency equation can be solved using matrix-product states (MPS) methods, as the influence matrix temporal entanglement is low. A combination of analytical insights and MPS computations allows us to characterize the structure of the influence matrix in terms of an effective “statistical-mechanics” description. We finally illustrate the predictive power of this description by analytically computing how quickly an embedded impurity spin thermalizes. The influence matrix approach formulated here provides an intuitive view of the quantum many-body dynamics problem, opening a path to constructing models of thermalizing dynamics that are solvable or can be efficiently treated by MPS-based methods and to further characterizing quantum ergodicity or lack thereof.
format	article
author	Alessio Lerose Michael Sonner Dmitry A. Abanin
author_facet	Alessio Lerose Michael Sonner Dmitry A. Abanin
author_sort	Alessio Lerose
title	Influence Matrix Approach to Many-Body Floquet Dynamics
title_short	Influence Matrix Approach to Many-Body Floquet Dynamics
title_full	Influence Matrix Approach to Many-Body Floquet Dynamics
title_fullStr	Influence Matrix Approach to Many-Body Floquet Dynamics
title_full_unstemmed	Influence Matrix Approach to Many-Body Floquet Dynamics
title_sort	influence matrix approach to many-body floquet dynamics
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/b354174a64d84de1978bfb910325e0a8
work_keys_str_mv	AT alessiolerose influencematrixapproachtomanybodyfloquetdynamics AT michaelsonner influencematrixapproachtomanybodyfloquetdynamics AT dmitryaabanin influencematrixapproachtomanybodyfloquetdynamics
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Influence Matrix Approach to Many-Body Floquet Dynamics

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