Hyperspherical theory of the quantum Hall effect: the role of exceptional degeneracy

Abstract

By separating the Schrödinger equation for $N$ noninteracting spin-polarized fermions in two-dimensional hyperspherical coordinates, we demonstrate that fractional quantum Hall (FQH) states emerge naturally from degeneracy patterns of the antisymmetric free-particle eigenfunctions. In the presence of Coulomb interactions, the FQH states split off from a degenerate manifold and become observable as distinct quantized energy eigenstates with an energy gap. This alternative classification scheme is based on an approximate separability of the interacting $N$-fermion Schrödinger equation in the hyperradial coordinate, which sheds light on the emergence of Laughlin states as well as other FQH states. An approximate good collective quantum number, the grand angular momentum $K$ from $K$-harmonic few-body theory, is shown to correlate with known FQH states at many filling factors observed experimentally.

15 pages, 10 figures, 3 tables

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Cited by in corpus (7)

• Universal few-body physics and cluster formation
• A Comprehensive Study of the Three- and Four-Neutron Systems at Low Energies
• Few-body correlations in two-dimensional Bose and Fermi ultracold mixtures
• Three and four identical fermions near the unitary limit
• Hyperspherical approach to the three-bosons problem in 2D with a magnetic field
• Few-body collective excitations beyond Kohn's theorem in quantum Hall systems
• Hyperspherical Slater determinant approach to few-body fractional quantum Hall states