Quantum Group and Magnetic Translations:. Bethe Ansatz Solution for the HARPER’S Equation
Abstract
We present the Bethe ansatz solution for the problem of Bloch electrons in magnetic field described by the Harper’s equation \[ \psi_{n+1} + \psi_{n-1} + 2\lambda\cos (k+n\Phi)\psi_n = E\psi_n\,. \] We made explicit a natural relation between magnetic translations and the quantum group Uq(sl2) and express the midband spectrum and the Bloch function in terms of solutions of the Bethe ansatz equations. In this letter we present solution for the critical value λ=1.
- Publication:
-
Modern Physics Letters B
- Pub Date:
- 1994
- DOI:
- 10.1142/S0217984994000315
- arXiv:
- arXiv:cond-mat/9310017
- Bibcode:
- 1994MPLB....8..311W
- Keywords:
-
- Condensed Matter
- E-Print:
- 9 pages, Revtex