Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice

TL;DR

This paper investigates the Kane-Mele-Hubbard model on a $\pi$-flux honeycomb lattice, revealing rich topological phases, magnetic order, and interaction-driven gaps through theoretical analysis and quantum Monte Carlo simulations.

Contribution

It introduces the $\pi$-flux Kane-Mele-Hubbard model, analyzing its topological properties, magnetic phases, and interaction effects, including the prediction and confirmation of correlation-induced gaps.

Findings

Noninteracting bands have Chern number $C= ext{±}2$

Magnetically ordered phase extends to weak coupling

Interaction induces a correlation gap confirmed by simulations

Abstract

We consider the Kane-Mele-Hubbard model with a magnetic $\pi$ flux threading each honeycomb plaquette. The resulting model has remarkably rich physical properties. In each spin sector, the noninteracting band structure is characterized by a total Chern number $C=\pm 2$. Fine-tuning of the intrinsic spin-orbit coupling $\lambda$ leads to a quadratic band crossing point associated with a topological phase transition. At this point, quantum Monte Carlo simulations reveal a magnetically ordered phase which extends to weak coupling. Although the spinful model has two Kramers doublets at each edge and is explicitly shown to be a $Z_{2}$ trivial insulator, the helical edge states are protected at the single-particle level by translation symmetry. Drawing on the bosonized low-energy Hamiltonian, we predict a correlation-induced gap as a result of umklapp scattering for half-filled bands. For strong interactions, this prediction is confirmed by quantum Monte Carlo simulations.