Hyperbolic Supersymmetric Quantum Hall Effect
Kazuki Hasebe
TL;DR
This paper develops a supersymmetric quantum Hall effect model on a super-hyperboloid using group theory, analyzing single-particle and many-body phenomena, and revealing fuzzy super-hyperboloid structures in the lowest Landau level.
Contribution
It introduces a non-compact SUSY Hopf map and formulates the quantum Hall effect on a super-hyperboloid, including wavefunctions and topological excitations.
Findings
Landau problem on super-hyperboloid solved
Laughlin wavefunction derived for supersymmetric case
Fuzzy super-hyperboloid appears in lowest Landau level
Abstract
Developing a non-compact version of the SUSY Hopf map, we formulate the quantum Hall effect on a super-hyperboloid. Based on group theoretical methods, we first analyze the one-particle Landau problem, and successively explore the many-body problem where Laughlin wavefunction, hard-core pseudo-potential Hamiltonian and topological excitations are derived. It is also shown that the fuzzy super-hyperboloid emerges in the lowest Landau level.
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