Quantum Group and Magnetic Translations. Bethe-Ansatz Solution for Bloch Electrons in a Magnetic Field

Abstract

We present a new approach to the problem of Bloch electrons in magnetic field,\\ by making explicit a natural relation between magnetic translations and the\\quantum group $U_q(s{l}_2)$. The approach allows to express the spectrum and\\\ the Bloch function as solutions of the Bethe-Ansatz equations typical for com\\pletely integrable quantum systems

9 pages, Revtex

Cited by in corpus (7)

• Algebraization of difference eigenvalue equations related to $U_q(s{l}_2)$
• Hierarchical Structure of Azbel-Hofstader Problem: Strings and loose ends of Bethe Ansatz
• Bethe ansatz for the Harper equation: Solution for a small commensurability parameter
• Landau Levels from the Bethe Ansatz Equations
• Hofstadter problem in higher dimensions
• Golden mean renormalization for the almost Mathieu operator and related skew products
• Azbel-Hofstadter model on triangular lattice revisited