Dimensional Reduction of a Generalized Flux Problem

Details Dimensional Reduction of a Generalized Flux Problem Dimensional Reduction of a Generalized Flux Problem

1992-06-18

arxiv.org/abs/cond-mat/9206005v1

Mod.Phys.Lett. B6 (1992) 717-728

Physics

Condensed Matter

19 pages, preprint ETH-TH 92/09 (to appear in Mod. Phys. Lett. B)

Scientific paper

10.1142/S021798499200079X

A generalized flux problem with Abelian and non-Abelian fluxes is considered. In the Abelian case we shall show that the generalized flux problem for tight-binding models of noninteracting electrons on either $2n$ or $2n+1$ dimensional lattice can always be reduced to a $n$ dimensional hopping problem. A residual freedom in this reduction enables to identify equivalence classes of hopping Hamiltonians which have the same spectrum. In the non-Abelian case the reduction is not possible in general unless the flux tensor factorizes into an Abelian one times an element of the corresponding algebra.

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