Multiple Edge Partition Functions For Fractional Quantum Hall States

TL;DR

This paper develops a method to compute multiple edge partition functions for fractional quantum Hall states using conformal field theory and the Verlinde formula, providing insights into edge state constraints.

Contribution

It introduces a novel approach to analyze multiple edge states in fractional quantum Hall systems via conformal field theory and vertex operators, deriving partition functions with the Verlinde formula.

Findings

Derived multiple edge partition functions for Laughlin and Pfaffian states.

Demonstrated the role of conformal field theory in constraining edge states.

Provided a framework for analyzing edge state interactions in quantum Hall systems.

Abstract

We consider the multiple edge states of the Laughlin state and the Pfaffian state. These edge states are globally constrained through the operator algebra of conformal field theory in the bulk. We analyze these constraints by introducing an expression of quantum hall state by the chiral vertex operators and obtain the multiple edge partition functions by using the Verlinde formula.