Unification of Laughlin and Moore–Read states in SUSY quantum Hall effect

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 stereographically 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.