Bloch Electron in a Magnetic Field : Diagonalization of Tight-Binding Models

Abstract

A connection of a variety of tight-binding models of noninteracting electrons on a rectangular lattice in a magnetic field with theta functions is established. A new spectrum generating symmetry is discovered which essentialy reduces the problem of diagonalization of these models. Provided that one knows one eigenvector at one point in the parameter space of the corresponding Harper equation one knows an eigenfunction of the corresponding model in the whole range of momentum singlet out by the Landau gauge.