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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.

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Correspondence to Marcello Porta.

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Communicated by M. Salmhofer

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Giuliani, A., Mastropietro, V. & Porta, M. Universality of the Hall Conductivity in Interacting Electron Systems. Commun. Math. Phys. 349, 1107–1161 (2017). https://doi.org/10.1007/s00220-016-2714-8

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  • DOI: https://doi.org/10.1007/s00220-016-2714-8