Short-ranged interaction effects onZ2topological phase transitions

Abstract

We develop an analytical approach based on a combined perturbative and self-consistent mean-field treatment of interactions that is capable of capturing topological phase transitions beyond either method when used independently. As an illustration of the method, we study the effects of short-range interactions on the ${Z}_{2}$ topological insulator phase, also known as the quantum spin Hall phase, in two generalized versions of the Kane-Mele model at half-filling on the honeycomb lattice. The results are in excellent agreement with quantum Monte Carlo calculations on the same model and cannot be reproduced by either a perturbative treatment or a self-consistent mean-field treatment of the interactions. Our analytical approach helps to clarify how the symmetries of the one-body terms of the Hamiltonian determine whether interactions tend to stabilize or destabilize a topological phase. Moreover, our method should be applicable to a wide class of models where topological transitions due to interactions are in principle possible but are not correctly predicted by either perturbative or self-consistent treatments.