  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.
