# Phase diagram of the Kane-Mele Coulomb model

Speaker:
F. F. Assaad (Wurzburg University, Germany)
Date:
Wed, 01/10/2014 - 11:00am to 12:00pm
Location:
Theory Commons (S16 level 6)
Host:
The fact that in graphene the density of states vanishes at the Fermi level invalidates the usual arguments for the screening of the nonlocal part of the long-range Coulomb repulsion.  Consequently, the latter has to be taken into account for a realistic modeling of correlation effects. Here, we solve the Kane-Mele model with an additional Coulomb repulsion using auxiliary-field quantum Monte Carlo techniques on lattices with up to $18 \times 18$ unit cells. The Coulomb repulsion favors short-range sublattice charge fluctuations which compete with the onset of antiferromagnetic order driven by the onsite repulsion. As a result, in the model with onsite and nonlocal repulsion, the critical interaction for the transition to the antiferromagnetic phase is significantly enhanced. However,  the overall topology of the phase diagrams remains unchanged upon including a long-ranged Coulomb tail.   A systematic finite-size scaling is consistent with the view that, similar to the case of a Hubbard interaction, the transition from the quantum spin Hall phase to the antiferromagnet falls into the 3D XY universality class, and that the transition from the semimetal to the antiferromagnetic insulator is of the Gross-Neveu  Heisenberg type. Hence, the long-ranged Coulomb repulsion is (marginally) irrelevant for the  considered model.