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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Abstract
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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