An SU(2) Analog of the Azbel--Hofstadter Hamiltonian

Abstract

Motivated by recent findings due to Wiegmann and Zabrodin, Faddeev and Kashaev concerning the appearence of the quantum U_q(sl(2)) symmetry in the problem of a Bloch electron on a two-dimensional magnetic lattice, we introduce a modification of the tight binding Azbel--Hofstadter Hamiltonian that is a specific spin-S Euler top and can be considered as its ``classical'' analog. The eigenvalue problem for the proposed model, in the coherent state representation, is described by the S-gap Lamé equation and, thus, is completely solvable. We observe a striking similarity between the shapes of the spectra of the two models for various values of the spin S.

19 pages, LaTeX, 4 PostScript figures. Relation between Cartan and Cartesian deformation of SU(2) and numerical results added. Final version as will appear in J. Phys. A: Math. Gen

References in corpus (4)

• Quantum Group and Magnetic Translations. Bethe-Ansatz Solution for Azbel-Hofstadter Problem
• Generalized Bethe Ansatz Equations for Hofstadter Problem
• Holomorphic Quantization on the Torus and Finite Quantum Mechanics
• q-Ultraspherical polynomials for q a root of unity

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