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Aperiodically Driven Integrable Systems and Their Emergent Steady States

Nandy, Sourav and Sen, Arnab and Sen, Diptiman (2017) Aperiodically Driven Integrable Systems and Their Emergent Steady States. In: PHYSICAL REVIEW X, 7 (3).

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Official URL: http://doi.org/10.1103/PhysRevX.7.031034

Abstract

Does a closed quantum many-body system that is continually driven with a time-dependent Hamiltonian finally reach a steady state? This question has only recently been answered for driving protocols that are periodic in time, where the long-time behavior of the local properties synchronizes with the drive and can be described by an appropriate periodic ensemble. Here, we explore the consequences of breaking the time-periodic structure of the drive with additional aperiodic noise in a class of integrable systems. We show that the resulting unitary dynamics leads to new emergent steady states in at least two cases. While any typical realization of random noise causes eventual heating to an infinite-temperature ensemble for all local properties in spite of the system being integrable, noise that is self-similar in time leads to an entirely different steady state (which we dub the ``geometric generalized Gibbs ensemble'') that emerges only after an astronomically large time scale. To understand the approach to the steady state, we study the temporal behavior of certain coarse-grained quantities in momentum space that fully determine the reduced density matrix for a subsystem with size much smaller than the total system. Such quantities provide a concise description for any drive protocol in integrable systems that are reducible to a free-fermion representation.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the AMER PHYSICAL SOC, ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Depositing User: Id for Latest eprints
Date Deposited: 09 Sep 2017 04:28
Last Modified: 30 Sep 2018 12:30
URI: http://eprints.iisc.ac.in/id/eprint/57749

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