Conductance distribution at criticality: one‐dimensional Anderson model with random long‐range hopping

We study numerically the conductance distribution function w(T) for the one‐dimensional Anderson model with random long‐range hopping described by the Power‐law Banded Random Matrix model at criticality. We concentrate on the case of two single‐channel leads attached to the system. We observe a smooth transition from localized to delocalized behavior in the conductance distribution by increasing b, the effective bandwidth of the model. Also, for b < 1 we show that w(ln T/T typ ) is scale invariant, where T typ = exp 〈 ln T 〉 is the typical value of T. Moreover, we find that for T < T typ , w(ln T/T typ ) shows a universal behavior proportional to (T/T typ ) ‐1/2 .