Influence of interactions on the anomalous quantum Hall effect

C. X. Zhang, M. A. Zubkov

Published 2019-02-18Version 1

We investigate the influence of interactions on the anomalous quantum Hall conductivity within the framework of the particular tight - binding models of the $2+1$ D topological insulator and the $3+1$ D Weyl semimetal. Several types of interactions are considered including the contact four - fermion interactions, Yukawa and Coulomb interactions. Is is shown that when the considered interactions are taken into account in the one - loop approximation, the Hall conductivity for the insulator is the topological invariant in momentum space composed of the complete two - point Green function of the interacting model. It remains robust to the smooth modification of the system. For the Weyl semimetal the Hall conductivity is given by the similar expression composed of the two - point interacting Green function. It inherits the algebraic structure of the corresponding topological invariant of an insulator, but may vary continuously under smooth modifications of the system. We also demonstrate that the interactions may lead to the topological phase transitions accompanied by the change of Hall conductivity.