A Plasma Analogy and Berry Matrices for Non-Abelian Quantum Hall States

TL;DR

This paper introduces a plasma analogy and Berry matrix approach to compute non-Abelian quasihole statistics in quantum Hall states, linking conformal field theory and plasma models to reveal fractional charge and statistics.

Contribution

It develops a novel plasma analogy framework using conformal field theory to analyze non-Abelian quantum Hall states, providing new insights into quasihole statistics.

Findings

Berry phases confirm fractional charge of quasiholes

Two-quasihole state exhibits abelian statistics

Method derives non-Abelian statistics from plasma analogy

Abstract

We present an approach to the computation of the non-Abelian statistics of quasiholes in quantum Hall states, such as the Pfaffian state, whose wavefunctions are related to the conformal blocks of minimal model conformal field theories. We use the Coulomb gas construction of these conformal field theories to formulate a plasma analogy for the quantum Hall states. A number of properties of the Pfaffian state follow immediately, including the Berry phases which demonstrate the quasiholes' fractional charge, the abelian statistics of the two-quasihole state, and equal-time ground state correlation functions. The non-Abelian statistics of multi-quasihole states follows from an additional assumption.