Supersymmetric Quantum Hall Liquid with a Deformed Supersymmetry

Details Supersymmetric Quantum Hall Liquid with a Deformed Supersymmetry Supersymmetric Quantum Hall Liquid with a Deformed Supersymmetry

2009-01-13

arxiv.org/abs/0901.1724v2

Phys.Atom.Nucl.73:345-351, 2010

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, contribution to the proceedings of the Group 27 conference, Yerevan, Armenia, August 13-19, 2008, published version

Scientific paper

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.

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