Quantum group and magnetic translations Bethe ansatz for the Asbel-Hofstadter problem
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 U q(sl 2). 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 U q(sl 2).
- Publication:
-
Nuclear Physics B
- Pub Date:
- July 1994
- DOI:
- 10.1016/0550-3213(94)90443-X
- arXiv:
- arXiv:cond-mat/9312088
- Bibcode:
- 1994NuPhB.422..495W
- Keywords:
-
- Condensed Matter;
- High Energy Physics - Theory
- E-Print:
- 19 pages, Revtex