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 pseudopotential Hamiltonian whose groundstate is exactly the parameter-dependent supersymmetric Laughlin wavefunction. Though the SUSY pseudopotential Hamiltonian is parameter-dependent and non-Hermitian, its eigenvalues are parameter-independent and real.
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