From Irrational to Non-Unitary: on the Haffnian and Haldane-Rezayi wave functions

TL;DR

This paper explores the Haffnian and Haldane-Rezayi quantum Hall wave functions, revealing their connection through root configurations and generalized Pauli principles, which may shed light on the theory behind the irrational Haffnian state.

Contribution

It introduces a unified framework using root configurations and generalized Pauli principles to analyze and connect these quantum Hall states.

Findings

Established a link between Haffnian and Haldane-Rezayi states

Developed a generalized Pauli principle for counting degeneracies

Provided insights into the theory of the irrational Haffnian state

Abstract

We study the Haffnian and Haldane-Rezayi quantum Hall wave functions and their quasihole excitations by means of their `root configurations', and point out a close connection between these seemingly different states. For both states, we formulate a `generalized Pauli-principle', which allows to count the degeneracies of these states. The connection between these states might elucidate the underlying theory describing the `irrational' Haffnian state.