Quantum Monte Carlo simulation of the triangular lattice in the repulsive Hubbard model

The repulsive Hubbard model for the triangular lattice in two dimensions is studied by means of a quantum Monte Carlo simulation in the grand canonical ensemble. Both on-site and nearest neighbor Coulomb interactions are taken into account. The one-electron spectral function A(kω) is shown to gradually develop a gap as the temperature is lowered provided the Hubbard U is larger than the bandwidth. Analysis of the spin and charge structure factors (static correlation functions) shows that, while the charge factor remains featureless, the spin factor develops a strong peak very close to the M′ point (2π/3,0) of the small surface Brillouin zone (corresponding to the three-sublattice model). Implications for the behavior of the 3×3 adlayer structures on fourth-group semiconductor surfaces are briefly commented upon.