Universality of the Hall conductivity in interacting electron systems

Abstract

We prove the quantization of the Hall conductivity for general weakly interacting gapped fermionic systems on two-dimensional periodic lattices. The proof is based on fermionic cluster expansion techniques combined with lattice Ward identities, and on a reconstruction theorem that allows us to compute the Kubo conductivity as the analytic continuation of its imaginary time counterpart.

58 pages, 4 figures. v3: final version, accepted for publication on Comm. Math. Phys

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