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

TL;DR

This paper introduces a stochastic functional approach to analyze the Mott transition in the Kane-Mele-Hubbard model, revealing insights into the topological and magnetic properties of the phase transition.

Contribution

It develops a variational principle-based equation to describe the Mott transition in an interacting topological insulator, incorporating charge and spin channels.

Findings

The band gap remains finite at the transition.

The Mott phase exhibits antiferromagnetism in the x-y plane.

The topological phase is characterized by a $_2$ number related to edge modes.

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. The band gap remains finite at the transition and the Mott phase is characterized by antiferromagnetism in the $x-y$ 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.