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

TL;DR

This paper demonstrates that the transport properties of quantum wires with off-diagonal disorder are nonuniversal due to the dependence on two parameters, explained through a geometric perspective involving the transfer matrix group.

Contribution

It introduces a geometric framework showing the nonuniversality of localization in quantum wires with off-diagonal disorder by analyzing the transfer matrix group structure.

Findings

Transport properties depend on two parameters: mean free path and an additional parameter.

Existing single-parameter scaling equation is a special case within a broader family.

Numerical simulations support the geometric explanation of nonuniversality.

Abstract

It is shown that, in the scaling regime, transport properties of quantum wires with off-diagonal disorder are described by a family of scaling equations that depend on two parameters: the mean free path and an additional continuous parameter. The existing scaling equation for quantum wires with off-diagonal disorder [Brouwer et al., Phys. Rev. Lett. 81, 862 (1998)] is a special point in this family. Both parameters depend on the details of the microscopic model. Since there are two parameters involved, instead of only one, localization in a wire with off-diagonal disorder is not universal. We take a geometric point of view and show that this nonuniversality follows from the fact that the group of transfer matrices is not semi-simple. Our results are illustrated with numerical simulations for a tight-binding model with random hopping amplitudes.