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Drude weight fluctuations in many-body localized systems

Michele Filippone

Many-body localized systems are supposed to be perfectly insulating for temperatures below a critical temperature Tc. In this talk, we will discuss some of the transport properties of systems showing a transition to a many-body localized phase. In particular, we numerically investigate the distribution of Drude weights D of many-body states in disordered one-dimensional interacting electron systems across the transition. Drude weights are proportional to the spectral curvatures induced by magnetic fluxes in mesoscopic rings. They offer a method to relate the transition to the many-body localized phase to transport properties. In the delocalized regime, we find that the Drude weight distribution at a fixed disorder configuration agrees well with the random-matrix-theory prediction P(D)∝ (γ^2+D^2)^(-3/), although the distribution width γ strongly fluctuates between disorder realizations. A crossover is observed towards a distribution with different large-D asymptotics deep in the many-body localized phase, which remarkably is not reproduced by the expected Cauchy distribution. We show that the average distribution width <γ>, rescaled by LΔ, Δ being the average level spacing in the middle of the spectrum and L the systems size, is an efficient probe of the many-body localization transition, as it increases/vanishes exponentially in the delocalized/localized phase.

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