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Dimensional Reduction of a Generalized Flux Problem

Alexander Moroz
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Abstract

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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Alexander Moroz. 1992-06-18. Dimensional Reduction of a Generalized Flux Problem. https://doi.org/10.1142/s021798499200079x

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