Quantum group and magnetic translations Bethe ansatz for the Asbel-Hofstadter problem

P. B. Wiegmann, A. V. Zabrodin

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65 Citations (Scopus)

Abstract

We present a new approach to the problem of Bloch electrons in a magnetic field (sometimes called the Asbel-Hofstadter problem), by making explicit a natural relation between the group of magnetic translations and the quantum group Uq(sl2). The approach allows us to express the "mid"-band spectrum of the model and the Bloch wave function as solutions of the Bethe ansatz equations typical for completely integrable quantum systems. The zero-mode wave functions are found explicitly in terms of q-deformed classical orthogonal polynomials. In this paper we present a solution for the isotropic problem. We also present a class of solvable quasiperiodic equations related to Uq(sl2).

Original languageEnglish
Pages (from-to)495-514
Number of pages20
JournalNuclear Physics B
Volume422
Issue number3
DOIs
Publication statusPublished - 11 Jul 1994
Externally publishedYes

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