Coulomb gas representation of quantum Hall effect on Riemann surfaces

TL;DR

This paper derives Laughlin wavefunctions for the quantum Hall effect on Riemann surfaces using Coulomb gas models, extending the plasma analogy and including quasihole states.

Contribution

It introduces a Coulomb gas framework to construct quantum Hall wavefunctions on Riemann surfaces with Poincare metric, generalizing previous flat-space results.

Findings

Laughlin wavefunctions on Riemann surfaces derived

Quasihole wavefunctions constructed

Plasma analogy discussed

Abstract

Using the correlation function of chiral vertex operators of the Coulomb gas model, we find the Laughlin wavefunctions of quantum Hall effect, with filling factor $\nu =1/m$, on Riemann sufaces with Poincare metric. The same is done for quasihole wavefunctions. We also discuss their plasma analogy.