Chiral Partition Functions of Quantum Hall Droplets

TL;DR

This paper derives chiral partition functions for quantum Hall droplets, linking conformal field theory to observable edge excitations and conductance peak patterns, enabling experimental tests of theoretical models.

Contribution

It provides explicit derivations of partition functions for various quantum Hall states and connects them to measurable conductance phenomena.

Findings

Peak patterns for Abelian hierarchical states identified

Peak patterns for non-Abelian Read-Rezayi states characterized

Comparison suggests experimental tests of conformal field theory properties

Abstract

Chiral partition functions of conformal field theory describe the edge excitations of isolated Hall droplets. They are characterized by an index specifying the quasiparticle sector and transform among themselves by a finite-dimensional representation of the modular group. The partition functions are derived and used to describe electron transitions leading to Coulomb blockade conductance peaks. We find the peak patterns for Abelian hierarchical states and non-Abelian Read-Rezayi states, and compare them. Experimental observation of these features can check the qualitative properties of the conformal field theory description, such as the decomposition of the Hilbert space into sectors, involving charged and neutral parts, and the fusion rules.