Spin-singlet hierarchy in the fractional quantum Hall effect

TL;DR

This paper proposes a new hierarchy of fractional quantum Hall states based on the Haldane-Rezayi state, providing a conformal field theory description and suggesting experimental tests for the observed odd denominator plateaux.

Contribution

It introduces a novel hierarchy framework for quantum Hall states involving the Haldane-Rezayi state and offers a conformal field theory perspective.

Findings

Permanent states are formed by integer quantum Hall effects on the Haldane-Rezayi state.

The odd denominator plateaux near ν=5/2 are explained as permanent states if ν=5/2 is the Haldane-Rezayi state.

No hierarchy is found on other candidate states for ν=5/2.

Abstract

We show that the so-called permanent quantum Hall states are formed by the integer quantum Hall effects on the Haldane-Rezayi quantum Hall state. Novel conformal field theory description along with this picture is deduced. The odd denominator plateaux observed around $\nu=5/2$ are the permanent states if the $\nu=5/2$ plateau is the Haldane-Rezayi state. We point out that there is no such hierarchy on other candidate states for $\nu=5/2$. We propose experiments to test our prediction.