Rational sequences for the conductance in quantum wires from affine Toda field theories

TL;DR

This paper derives a simple high-temperature formula for conductance in quantum wires modeled by affine Toda field theories, revealing rational sequences related to the fractional quantum Hall effect.

Contribution

It introduces a novel approach connecting affine Toda field theories with quantum conductance, deriving rational filling fractions from scattering data and thermodynamic Bethe ansatz.

Findings

Recovered Jain sequence fractions for specific affine Toda models

Established a link between scattering matrices and conductance sequences

Provided a new framework for analyzing quantum wire conductance

Abstract

We analyse the expression for the conductance of a quantum wire which is decribed by an integrable quantum field theory. In the high temperature regime we derive a simple formula for the filling fraction. This expression involves only the inverse of a matrix which contains the information of the asymptotic phases of the scattering matrix and the solutions of the constant thermodynamic Bethe ansatz equations. Evaluating these expressions for minimal affine Toda field theory we recover several sequences of rational numbers, which are multiples of the famous Jain sequence for the filling fraction occurring in the context of the fractional quantum Hall effect. For instance we obtain $\nu= 4 m/(2m +1)$ for $A_{4m-1}$-minimal affine Toda field theory. The matrices involved have in general non-rational entries and are not part of previous classification schemes based on integral lattices.