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 comparative analysis of two different types of variational wave functions with and without translational symmetry breaking reveals that the system undergoes a phase transition at V-c/t greater than or similar to 12, accompanied by the reconstruction of the Fermi surface. The existence of three-sublattice long-range order in the strong coupling region is confirmed by the finite-size scaling analysis. The 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. We also find the charge-density-wave-like state only for the symmetry broken wave functions at V < V-c which, however, possibly remains its a short-range order in the bulk limit, and is distinguished front the pinball liquid characterized by the large value of V-c/t.