Phase diagram of the Kane-Mele-Coulomb model

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.

9 pages, 7 figures

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• Temperature and doping induced instabilities of the repulsive Hubbard model on Lieb lattice
• Numerical stabilization of entanglement computation in auxiliary field quantum Monte Carlo simulations of interacting many-fermion systems
• Spontaneous particle-hole symmetry breaking of correlated fermions on the Lieb lattice
• Rashba coupling and magnetic order in correlated helical liquids
• Interplay between the edge-state magnetism and long-range Coulomb interaction in zigzag graphene nanoribbons: quantum Monte Carlo study
• Nature of continuous phase transitions in interacting topological insulators
• Benchmark study of an auxiliary-field quantum Monte Carlo technique for the Hubbard model with shifted-discrete Hubbard-Stratonovich transformations
• Quantum Monte Carlo simulation of topological phase transitions
• Quantum Monte Carlo study of the metal to insulator transition on a honeycomb lattice with 1/r interactions
• Short-ranged interaction effects on $Z_2$ topological phase transitions: The perturbative mean-field method