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Dynamical relaxation of correlators in periodically driven integrable quantum systems

Dec 6, 2021

14 pages

Published in:

Phys.Rev.B 105 (2022) 10, 104303

Published: Mar 1, 2022

e-Print:

2112.02915 [cond-mat.stat-mech]

DOI:

10.1103/PhysRevB.105.104303 (publication)

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Abstract: (APS)

We show that the correlation functions of a class of periodically driven integrable closed quantum systems approach their steady-state value as

n^{- (α + 1) / β}

, where

n

is the number of drive cycles and

α

and

β

denote positive integers. We find that, generically,

β = 2

within a dynamical phase characterized by a fixed

α

; however, its value can change to

β = 3

or

β = 4

either at critical drive frequencies separating two dynamical phases or at special points within a phase. We show that such decays are realized in both driven Su-Schrieffer-Heeger (SSH) and one-dimensional (1D) transverse field Ising models, discuss the role of symmetries of the Floquet spectrum in determining

β

, and chart out the values of

α

and

β

realized in these models. We analyze the SSH model for a continuous drive protocol using a Floquet perturbation theory which provides analytical insight into the behavior of the correlation functions in terms of its Floquet Hamiltonian. This is supplemented by an exact numerical study of a similar behavior for the 1D Ising model driven by a square pulse protocol. For both models, we find a crossover timescale

n_{c}

which diverges at the transition. We also unravel a long-time oscillatory behavior of the correlators when the critical drive frequency,

ω_{c}

, is approached from below

(ω < ω_{c})

. We tie such behavior to the presence of multiple stationary points in the Floquet spectrum of these models and provide an analytic expression for the time period of these oscillations.

Note:

v1; 16 pages, 8 figs

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Figures(15)

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