Title: 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 non-interacting 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/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 non-interacting localized phase where some memory is
always preserved.