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Dynamical relaxation of correlators in periodically driven integrable quantum systems

Aditya, S and Samanta, S and Sen, A and Sengupta, K and Sen, D (2022) Dynamical relaxation of correlators in periodically driven integrable quantum systems. In: Physical Review B, 105 (10).

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Official URL: https://doi.org/10.1103/PhysRevB.105.104303


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 nc which diverges at the transition. We also unravel a long-time oscillatory behavior of the correlators when the critical drive frequency, ωc, is approached from below (ω<ωc). 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.

Item Type: Journal Article
Publication: Physical Review B
Publisher: American Physical Society
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Hamiltonians; Ising model; Perturbation techniques; Quantum optics, Closed quantum system; Correlation function; Drive cycles; Dynamical phasis; Dynamical relaxation; Floquet spectrum; Positive integers; Quantum system; Steady-state values; Systems approach, Correlators
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 15 Jun 2022 09:59
Last Modified: 15 Jun 2022 09:59
URI: https://eprints.iisc.ac.in/id/eprint/73781

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