Phase diagram of the Kane-Mele-Coulomb model

TL;DR

This study maps the phase diagram of the Kane-Mele model with long-range Coulomb interactions using quantum Monte Carlo, revealing how nonlocal interactions influence magnetic and topological phases.

Contribution

It provides the first comprehensive phase diagram of the Kane-Mele-Coulomb model, highlighting the effects of long-range interactions on phase boundaries and universality classes.

Findings

Long-range Coulomb interactions increase the critical point for magnetic transition.

The phase diagram includes phases similar to the Kane-Mele-Hubbard model.

Transitions follow $SU(2)$ Gross-Neveu and 3D XY universality classes.

Abstract

We determine the phase diagram of the Kane-Mele model with a long-range Coulomb interaction using an exact quantum Monte Carlo method. Long-range interactions are expected to play a role in honeycomb materials because the vanishing density of states in the semimetallic weak-coupling phase suppresses screening. According to our results, the Kane-Mele-Coulomb model supports the same phases as the Kane-Mele-Hubbard model. The nonlocal part of the interaction promotes short-range sublattice charge fluctuations, which compete with antiferromagnetic order driven by the onsite repulsion. Consequently, the critical interaction for the magnetic transition is significantly larger than for the purely local Hubbard repulsion. Our numerical data are consistent with $SU(2)$ Gross-Neveu universality for the semimetal to antiferromagnet transition, and with 3D XY universality for the quantum spin Hall to antiferromagnet transition.