Bethe-ansatz for the Bloch electron in 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 ${\mathit{U}}_{\mathit{q}}$(${\mathit{sl}}_{2}$). The approach allows us to express the spectrum and the Bloch function as solutions of the Bethe-ansatz equations typical for completely integrable quantum systems.