Abstract:We consider a wide class of $2D$ tight - binding models of solid state physics. These models are, in the most general case, non - homogeneous. The topological invariant ${\cal N}_3$ responsible for the quantization of the Hall conductivity, for the specific case of the integer quantum Hall effect in $2D$, is expressed through the Wigner transformation of the two-point electron Matsubara Green function. We express this invariant as a pairing of the element of the $K^{-1}$ group (generated by the Green function) with the specific element of the cyclic cohomology group $HC^3$. According to a set of local index theorems the values of ${\cal N}_3$ can be shown to be integer for a limited class of tight - binding models.
From: Mikhail Zubkov Dr [view email]
[v1]
Sun, 7 Jun 2026 22:47:29 UTC (79 KB)
[v2]
Sun, 21 Jun 2026 21:05:19 UTC (91 KB)
[v3]
Mon, 27 Jul 2026 22:28:29 UTC (95 KB)
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