Exclusion statistics for quantum Hall states in Tao-Thouless limit

TL;DR

This paper investigates the exclusion statistics of quantum Hall states in the Tao-Thouless limit, identifying low-energy sectors and analyzing how these states evolve as the system approaches the physical regime.

Contribution

It introduces a detailed analysis of exclusion statistics for quantum Hall states in the Tao-Thouless limit and explores their evolution towards realistic conditions.

Findings

Low-energy sectors are well-defined for all filling factors.

Exclusion statistics is initially determined in the Tao-Thouless limit.

Exclusion statistics is modified as the system moves away from the Tao-Thouless limit.

Abstract

We consider spin-polarized abelian quantum Hall states in the Tao-Thouless limit, {\it ie} on a thin torus. For any filling factor $\nu=p/q$ a well-defined sector of low-energy states is identified and the exclusion statistics of the excitations is determined. We study numerically, at and near $\nu=1/3$ and $2/5$, how the low energy states develop as one moves away from the TT-limit towards the physical regime. We find that the lowest energy states in the physical regime develop from states in the low energy sector but that the exclusion statistics is modified.