The random magnetic flux problem in a quantum wire

TL;DR

This paper investigates the conductance properties of a quantum wire with random magnetic flux, revealing a new universality class at the band center with an even-odd effect in conductance decay.

Contribution

It introduces the chiral unitary symmetry class for quantum wires at the band center and analytically and numerically characterizes its unique conductance behavior.

Findings

At the band center, conductance follows a new universality class.

An even-odd effect in conductance decay is observed in the localized regime.

Analytical and numerical results agree on conductance moments.

Abstract

The random magnetic flux problem on a lattice and in a quasi one-dimensional (wire) geometry is studied both analytically and numerically. The first two moments of the conductance are obtained analytically. Numerical simulations for the average and variance of the conductance agree with the theory. We find that the center of the band $\epsilon=0$ plays a special role. Away from $\epsilon=0$, transport properties are those of a disordered quantum wire in the standard unitary symmetry class. At the band center $\epsilon=0$, the dependence on the wire length of the conductance departs from the standard unitary symmetry class and is governed by a new universality class, the chiral unitary symmetry class. The most remarkable property of this new universality class is the existence of an even-odd effect in the localized regime: Exponential decay of the average conductance for an even number of channels is replaced by algebraic decay for an odd number of channels.