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Universality of the Hall Conductivity in Interacting Electron Systems

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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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Authors and Affiliations

  1. Department of Mathematics and Physics, University of Roma Tre, L.go S. L. Murialdo 1, 00146, Rome, Italy

    Alessandro Giuliani

  2. Department of Mathematics “F. Enriquez”, University of Milano, Via C. Saldini 50, 20133, Milan, Italy

    Vieri Mastropietro

  3. Mathematics Department, University of Zürich, Winterthurerstrasse 190, 8057, Zurich, Switzerland

    Marcello Porta

Authors
  1. Alessandro Giuliani
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  2. Vieri Mastropietro
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  3. Marcello Porta
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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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