Quantum group and magnetic translations Bethe ansatz for the AsbelHofstadter problem
Abstract
We present a new approach to the problem of Bloch electrons in a magnetic field (sometimes called the AsbelHofstadter 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 zeromode wave functions are found explicitly in terms of qdeformed 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:
 10.1016/05503213(94)90443X
 arXiv:
 arXiv:condmat/9312088
 Bibcode:
 1994NuPhB.422..495W
 Keywords:

 Condensed Matter;
 High Energy Physics  Theory
 EPrint:
 19 pages, Revtex