Variational Monte Carlo Study of a Spinless Fermion t-V Model on a   Triangular Lattice: Formation of a Pinball Liquid
  We analyze a model of spinless fermions on a triangular lattice at half-filling interacting via strong nearest-neighbor repulsive interactions, V, using the variational Monte Carlo simulation technique. The existence of three-sublattice long-range order is confirmed by the finite-size scaling analysis of the charge structural factor at V_c/t > 12. This ordered phase shows characteristics expected for a so called "pinball liquid" state, which has the spontaneous separation of fermionic degrees of freedom into coexisting Wigner crystal-like charge order (pin) and a metal (ball). The pins are fixed in order to maximize the kinetic energy gain of balls which move almost freely. The Fermi surface is reconstructed at V=V_c and remains towards the strong coupling limit. These features reminiscent of the strong correlation together with the large value of V_c/t distinguishes the pinball liquid from the conventional charge-density-wave. 
M. Miyazaki, C. Hotta, S. Miyahara, K. Matsuda, and N. Furukawa