Fractional quantum Hall effect and nonabelian statistics

TL;DR

This paper explores the connection between fractional quantum Hall wavefunctions and conformal field theory, demonstrating how nonabelian statistics emerge, exemplified by the Pfaffian state related to the 2D Ising model.

Contribution

It establishes a framework linking fractional quantum Hall states to conformal blocks, enabling the construction of nonabelian statistics models from conformal field theory.

Findings

Fractional quantum Hall wavefunctions can be interpreted as conformal blocks.

Nonabelian statistics can be constructed from conformal field theory.

The Pfaffian state exhibits nonabelian anyonic excitations.

Abstract

It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. Fractional statistics can be extended to nonabelian statistics and examples can be constructed from conformal field theory. The Pfaffian state is related to the 2D Ising model and possesses fractionally charged excitations which are predicted to obey nonabelian statistics.