Hyperbolic Supersymmetric Quantum Hall Effect

Abstract

Developing a non-compact version of the SUSY Hopf map, we formulate the quantum Hall effect on a super-hyperboloid. Based on $OSp(1|2)$ 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.

14 pages, two columns, no figures, published version, typos corrected

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Cited by in corpus (17)

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• Split-Quaternionic Hopf Map, Quantum Hall Effect, and Twistor Theory
• Non-Compact Hopf Maps and Fuzzy Ultra-Hyperboloids
• N=4 Supersymmetry and the BPST Instanton
• $SO(4)$ Landau Models and Matrix Geometry
• The Split-Algebras and Non-compact Hopf Maps
• Landau Levels as a Limiting Case of a Model with the Morse-Like Magnetic Field
• A Quantum Ring in a Nanosphere
• Supersymmetric Extension of Hopf Maps: N=4 sigma-models and the S^3 -> S^2 Fibration
• $SO(5)$ Landau Model and 4D Quantum Hall Effect in The $SO(4)$ Monopole Background
• N=4 chiral supermultiplet interacting with a magnetic field
• N=8 superconformal mechanics: direct construction
• Symmetries of deformed supersymmetric mechanics on Kähler manifolds
• Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
• SU(2) reductions in N=4 multidimensional supersymmetric mechanics
• Superintegrable deformations of oscillator and Coulomb systems