Conductance and its universal fluctuations in the directed network model at the crossover to the quasi-one-dimensional regime

TL;DR

This paper investigates the universal conductance fluctuations in a directed network model representing chiral edge states on a cylindrical quantum Hall surface, analyzing the crossover from two-dimensional to one-dimensional regimes.

Contribution

It introduces a spin wave expansion approach to derive universal functions describing conductance crossovers in this model.

Findings

Derived universal functions for conductance mean and variance during crossover

Identified the first nontrivial order behavior of conductance fluctuations

Connected the directed network model to a 1D quantum ferromagnetic spin chain

Abstract

The directed network model describing chiral edge states on the surface of a cylindrical 3D quantum Hall system is known to map to a one-dimensional quantum ferromagnetic spin chain. Using the spin wave expansion for this chain, we determine the universal functions for the crossovers between the 2D chiral metallic and 1D metallic regimes in the mean and variance of the conductance along the cylinder, to first nontrivial order.