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

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

1995-08-22

arxiv.org/abs/hep-th/9508111v3

J.Phys.A31:3961-3975,1998

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, LaTeX, 4 PostScript figures. Relation between Cartan and Cartesian deformation of SU(2) and numerical results added.

Scientific paper

10.1088/0305-4470/31/17/007

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 Lam\'e 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.

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