Nonuniversality in quantum wires with off-diagonal disorder: a geometric point of view

It is shown that, in the scaling regime, transport properties of quantum wi res with off-diagonal disorder are described by a family of scaling equatio ns that depend on two parameters: the mean free path and an additional cont inuous parameter. The existing scaling equation for quantum wires with off- diagonal disorder [Brouwer et al., Phys. Rev. Lett. 81 (1998) 862] is a spe cial point in this family. Both parameters depend on the details of the mic roscopic model. Since there are two parameters involved, instead of only on e, localization in a wire with off-diagonal disorder is not universal. We t ake a geometric point of view and show that this non-universality follows f rom the fact that the group of transfer matrices is not semi-simple. Our re sults are illustrated with numerical simulations for a tight-binding model with random hopping amplitudes. (C) 2000 Elsevier Science B.V. All rights r eserved.