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)∝(γ2+D2)−3/2, 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 however differs from the commonly 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.
