Drude weight fluctuations in many-body localized systems

作者：Filippone Michele; Brouwer Piet W; Eisert Jens; von Oppen Felix

来源：Physical Review B, 2016, 94(20): 201112.

DOI：10.1103/PhysRevB.94.201112

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) alpha (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.

• 出版日期2016-11-18