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Characterizing Time Irreversibility in Disordered Fermionic Systems by the Effect of Local Perturbations

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De Tomasi,  Guiseppe
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Heyl,  Markus
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Pollmann,  Frank
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Vardhan, S., De Tomasi, G., Heyl, M., Heller, E. J., & Pollmann, F. (2017). Characterizing Time Irreversibility in Disordered Fermionic Systems by the Effect of Local Perturbations. Physical Review Letters, 119(1): 016802. doi:10.1103/PhysRevLett.119.016802.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002D-CEA1-F
Abstract
We study the effects of local perturbations on the dynamics of disordered fermionic systems in order to characterize time irreversibility. We focus on three different systems: the noninteracting Anderson and Aubry-Andre-Harper (AAH) models and the interacting spinless disordered t-V chain. First, we consider the effect on the full many-body wave functions by measuring the Loschmidt echo (LE). We show that in the extended or ergodic phase the LE decays exponentially fast with time, while in the localized phase the decay is algebraic. We demonstrate that the exponent of the decay of the LE in the localized phase diverges proportionally to the single-particle localization length as we approach the metal-insulator transition in the AAH model. Second, we probe different phases of disordered systems by studying the time expectation value of local observables evolved with two Hamiltonians that differ by a spatially local perturbation. Remarkably, we find that many-body localized systems could lose memory of the initial state in the longtime limit, in contrast to the noninteracting localized phase where some memory is always preserved.