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

E. G. Floratos; S. Nicolis

doi:10.1088/0305-4470/31/17/007

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arXiv · hep-th/9508111

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

E. G. Floratos·S. Nicolis

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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.

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E. G. Floratos, S. Nicolis. 1998-02-23. An SU(2) Analog of the Azbel--Hofstadter Hamiltonian. https://doi.org/10.1088/0305-4470%2F31%2F17%2F007

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