Advances in Theoretical and Mathematical Physics

Generalized TKNN-equations

Giuseppe De Nittis and Giovanni Landi

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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.

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Adv. Theor. Math. Phys., Volume 16, Number 2 (2012), 505-547.

First available in Project Euclid: 23 January 2013

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De Nittis, Giuseppe; Landi, Giovanni. Generalized TKNN-equations. Adv. Theor. Math. Phys. 16 (2012), no. 2, 505--547.

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