Universality of the Hall conductivity in Interacting electron systems

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. DOI: https://doi.org/10.1007/s00220-016-2714-8 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-128376 Accepted Version Originally published at: Giuliani, Alessandro; Mastropietro, Vieri; Porta, Marcello (2017). Universality of the Hall conductivity in Interacting electron systems. Communications in Mathematical Physics, 349(3):1107-1161. DOI: https://doi.org/10.1007/s00220-016-2714-8 Universality of the Hall conductivity in interacting electron systems Alessandro Giuliani University of Roma Tre, Department of Mathematics and Physics, L.go S. L. Murialdo 1, 00146 Roma, Italy Vieri Mastropietro University of Milano, Department of Mathematics “F. Enriquez”, Via C. Saldini 50, 20133 Milano, Italy Marcello Porta University of Zürich, Mathematics Department, Winterthurerstrasse 190, 8057 Zürich, Switzerland 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.