Chiral Metal as a Ferromagnetic Super Spin Chain

TL;DR

This paper provides an exact non-perturbative analysis of a disordered chiral metal model, revealing a supersymmetric spin chain representation and universal spectral correlations akin to random matrix theory.

Contribution

It introduces a supersymmetric spin chain model for disordered chiral metals and derives exact results for their spectral and diffusion properties.

Findings

Exact ground state and spin wave excitations identified.

Universal form of the density of states correlator derived.

Mapping to a supersymmetric ferromagnetic spin chain established.

Abstract

The electrons on the surface of a disordered multi-layer integer quantum Hall system constitute an unusual chiral metal with ballistic motion transverse to the field, and diffusive motion parallel to it. We present a non-perturbative analytic treatment of an appropriate model, consisting of disordered chiral Fermions in two dimensions. A supersymmetric generating functional is set up for the correlation functions of this system. The strong disorder limit is mapped into a supersymmetric spin chain, with ferromagnetic exchange coupling, reflecting the electron's chiral motion. The ferromagnetic ground state and the spin wave excitations, corresponding to the diffusion modes of the chiral metal, are found exactly. The parametric density of states correlator in the ergodic limit is computed from a Boltzmann-weighted sum over low energy spin states. The result is of a universal form and coincides with that for a Hermitian random matrix.