Supersymmetric Quantum Hall Liquid with a Deformed Supersymmetry

TL;DR

This paper develops a supersymmetric quantum Hall liquid with a deformed supersymmetry, interpolating between known wavefunctions, and constructs a related pseudo-potential Hamiltonian with real eigenvalues.

Contribution

It introduces a parameter-dependent supersymmetric Laughlin wavefunction with deformed supersymmetry and constructs a corresponding pseudo-potential Hamiltonian with real eigenvalues.

Findings

Wavefunction interpolates between Laughlin and Moore-Read states

Hamiltonian's eigenvalues are parameter-independent and real

Deformed supersymmetry is realized in the constructed model

Abstract

We construct a supersymmetric quantum Hall liquid with a deformed supersymmetry. One parameter is introduced in the supersymmetric Laughlin wavefunction to realize the original Laughlin wavefunction and the Moore-Read wavefunction in two extremal limits of the parameter. The introduced parameter corresponds to the coherence factor in the BCS theory. It is pointed out that the parameter-dependent supersymmetric Laughlin wavefunction enjoys a deformed supersymmetry. Based on the deformed supersymmetry, we construct a pseudo-potential Hamiltonian whose groundstate is exactly the parameter-dependent supersymmetric Laughlin wavefunction. Though the SUSY pseudo-potential Hamiltonian is parameter-dependent and non-Hermitian, its eigenvalues are parameter-independent and real.