Generalized TKNN-equations

Abstract

We derive generalized TKNN-equations via bundle representations of the noncommutative torus with rational deformation parameter, the bundle coming from spectral projections in the torus algebra. These equations relate Chern numbers of dual bundles, which we interpret as Hall conductances for Dirac-like Hamiltonians describing magnetic Bloch electrons in a strong magnetic field. We also present their generalizations for irrational values of the deformation parameter. © 2012 International Press.