@vindex10

On the equivalence of the Bott index and the Chern number on a torus, and the quantization of the Hall conductivity with a real space Kubo formula

. (2017)cite arxiv:1708.05912.

Abstract

The equivalence of the Bott index and the Chern number is established in the thermodynamic limit for a gapped, short ranged and bounded Hamiltonian on a two dimensional torus of linear size $ L $. A Kubo formula as an exact operatorial identity is provided in real space and used to show the quantization of the transverse conductance within corrections of order $L^-1$. In doing so the physical foundations of the theory that introduces the Bott index in the realm of condensed matter as proposed by Hastings and Loring in J. Math. Phys. (51), 015214, (2010) and Annals of Physics 326 (2011) 1699-1759 are recalled.

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On the equivalence of the Bott index and the Chern number on a torus, and the quantization of the Hall conductivity with a real space Kubo formula

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