Drude weight fluctuations in many-body localized systems

Abstract

We numerically investigate the distribution of Drude weights $D$ of many-body states in disordered one-dimensional interacting electron systems across the transition to a many-body localized phase. 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 $P(D)\propto ({\gamma }^2+D^2{)}^{-3/2}$, although the distribution width $\gamma$ 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 however differs from the commonly expected Cauchy distribution. We show that the average distribution width $⟨\gamma ⟩$, rescaled by $L\Delta$, $\Delta$ 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.

5 pages, 3 figures + 1 page Supplemental Material, 2 figures

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