Chiral Metal as a Heisenberg Ferromagnet

TL;DR

This paper maps the surface states of an integer quantum Hall multilayer onto a Heisenberg spin chain, revealing a highly anisotropic metallic behavior and analyzing conductance fluctuations and directed wave propagation.

Contribution

It introduces a non-perturbative mapping of quantum Hall surface states to a Heisenberg ferromagnet, providing new insights into their metallic properties and wave dynamics.

Findings

Surface states form a very anisotropic metal in the infinite size limit.

Conductance fluctuations are characterized for finite multilayer sizes.

Mean-square deflection of a directed wave grows as the square root of distance.

Abstract

The two dimensional surface of an integer quantum hall multilayer is mapped onto a Heisenberg spin-chain with ferromagnetic coupling. Using this mapping it is shown non-perturbatively that the surface states constitute a very anisotropic metal in the infinite size limit. For multilayers of finite size, two diffusive mesoscopic regimes are identified and the conductance fluctuations are calculated perturbatively for both. The Heisenberg spin-chain representation is used to study the directed wave problem and the exact result is obtained that the mean-square deflection of a directed wave grows as the square root of the propagation of the distance.