Haldane's Fractional Exclusion Statistics for Multicomponent Systems

TL;DR

This paper explores Haldane's fractional exclusion statistics in multicomponent systems, analyzing their thermodynamics, critical behavior, and connections to topological order, especially in one-dimensional and quantum Hall contexts.

Contribution

It extends fractional exclusion statistics to systems with internal degrees of freedom and links statistical interactions to conformal field theories and topological order.

Findings

Critical behavior described by $c=1$ conformal field theories.

Statistical interactions fully characterize conformal weights.

Statistical interactions relate to topological order in Chern-Simons theory.

Abstract

The idea of fractional exclusion statistics proposed by Haldane is applied to systems with internal degrees of freedom, and its thermodynamics is examined. In case of one dimension, various bulk quantities calculated show that the critical behavior of such systems can be described by $c=1$ conformal field theories and conformal weights are completely characterized by statistical interactions. It is also found that statistical interactions have intimate relationship with a topological order matrix in Chern-Simons theory for the fractional quantum Hall effect.