Conductance statistics for the power‐law banded random matrix model

We study numerically the conductance statistics of the one‐dimensional (1D) Anderson model with random long‐range hoppings described by the Power‐law Banded Random Matrix (PBRM) model. Within a scattering approach to electronic transport, we consider two scattering setups in absence and presence of direct processes: 2M single‐mode leads attached to one side and to opposite sides of 1D circular samples. For both setups we show that (i) the probability distribution of the logarithm of the conductance T behaves as $w(lnT)∝TM2/2,$ for $T⋘Ttyp = exp〈lnT〉,$ for both the critical and the non‐critical samples; and (ii) at criticality there is a smooth crossover from localized‐like to delocalized‐like behavior in the transport properties of the PBRM model by decreasing the fractality of its eigenstates.