Analytical approach for the Mott transition in the Kane-Mele-Hubbard model

Abstract

The description of interactions in strongly correlated topological phases of matter remains a challenge. Here, we develop a stochastic functional approach for interacting topological insulators including both charge and spin channels. We find that the Mott transition of the Kane-Mele-Hubbard model may be described by the variational principle with one equation. We present different views of this equation from the electron Green's function, the free-energy, and the Hellmann-Feynman theorem. In particular, we show the stability of the transition line towards fluctuations, in good agreement with numerical results. The band gap remains finite at the transition and the Mott phase is characterized by antiferromagnetism in the $x\text{\ensuremath{-}}y$ plane. The interacting topological phase is described through a ${\mathbb{Z}}_{2}$ number related to helical edge modes. Our results then show that improving stochastic approaches can give further insight on the understanding of interacting phases of matter.