Bethe-ansatz for the Bloch electron in magnetic field

P. B. Wiegmann; A. V. Zabrodin

doi:10.1103/PhysRevLett.72.1890

Bethe-ansatz for the Bloch electron in magnetic field

P. B. Wiegmann and A. V. Zabrodin

Phys. Rev. Lett. 72, 1890 – Published 21 March 1994

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 $U_{q}$ ( ${sl}_{2}$ ). 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.

Received 14 September 1993

DOI:https://doi.org/10.1103/PhysRevLett.72.1890

Authors & Affiliations

P. B. Wiegmann and A. V. Zabrodin

James Frank Institute and Enrico Fermi Institute of the University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois
Landau Insitute for Theoretical Physics, 2 Kosygina Str., Moscow 117954, Russia
Enrico Fermi Institute and Mathematical Disciplines Center of the University of Chicago, 5640 South Eillis Avenue, Chicago, Illinois 60637
the Institute of Chemical Physics, Kosygina St. 4, SU-117334, Moscow, Russia