Unification of Laughlin and Moore-Read States in SUSY Quantum Hall Effect

TL;DR

This paper demonstrates that Laughlin and Moore-Read states in SUSY quantum Hall effect are connected through a hidden supersymmetry transformation, unifying these states within a broader SUSY framework and revealing analogies with superfluidity.

Contribution

It introduces a SUSY-based unification of Laughlin and Moore-Read states, showing they are limits of a master wavefunction and exploring topological excitations within this formalism.

Findings

Laughlin and Moore-Read states are related by SUSY transformation.

SUSY Laughlin wavefunction acts as a master wavefunction.

Analogies between SUSY quantum Hall effect and superfluidity are established.

Abstract

Based on the recently proposed SUSY quantum Hall effect, we show that Laughlin and Moore-Read states are related by a hidden SUSY transformation. Regarding the SUSY Laughlin wavefunction as a master wavefunction, Laughlin and Moore-Read states appear as two extreme limits of component wavefunctions. Realizations of topological excitations on Laughlin and Moore-Read states are also discussed in the SUSY formalism. We develop a streographically projected formulation of the SUSY quantum Hall effect. With appropriate interpretation of Grassmann odd coordinates, we illustrate striking analogies between SUSY quantum Hall effect and superfluidity.