Quantum Hall wave functions on the torus

TL;DR

This paper provides explicit hierarchy wave functions for quantum Hall states on the torus, extending conformal field theory methods to include Laughlin, Jain series, and observed states like ν=4/11.

Contribution

It introduces a novel extension of conformal field theory techniques to construct quantum Hall wave functions on the torus geometry.

Findings

Explicit expressions for various hierarchy wave functions on the torus

Extension of CFT methods from disc to torus geometry

Includes recently observed states such as ν=4/11

Abstract

We present explicit expressions for a large set of hierarchy wave functions on the torus. Included are the Laughlin states, the states in the positive Jain series, and recently observed states at e.g. $\nu = 4/11$. The techniques we use constitute a nontrivial extension of the conformal field theory methods developed earlier to construct the corresponding wave functions in disc geometry.