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

Characterizing Time Irreversibility in Disordered Fermionic Systems by the Effect of Local... 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-André-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 long-time limit, in contrast to the noninteracting localized phase where some memory is always preserved. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review Letters American Physical Society (APS)

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

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

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-André-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 long-time limit, in contrast to the noninteracting localized phase where some memory is always preserved.
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Publisher
The American Physical Society
Copyright
Copyright © © 2017 American Physical Society
ISSN
0031-9007
eISSN
1079-7114
D.O.I.
10.1103/PhysRevLett.119.016802
Publisher site
See Article on Publisher Site

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-André-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 long-time limit, in contrast to the noninteracting localized phase where some memory is always preserved.

Journal

Physical Review LettersAmerican Physical Society (APS)

Published: Jul 7, 2017

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