Ground-state phase diagram of the triangular lattice Hubbard model by the density-matrix renormalization group method

Two-dimensional density-matrix renormalization group method is employed to examine the ground-state phase diagram of the Hubbard model on the triangular lattice at half-filling. The calculation reveals two discontinuities in the double occupancy with increasing the repulsive Hubbard interaction U at U-c1 similar to 7.8t and U-c2 similar to 9.9t (t being the hopping integral), indicating that there are three phases separated by first-order transitions. The absence of any singularity in physical quantities for 0 <= U < U-c1 implies a metallic phase in this regime. For U > U-c2, the local spin density induced by an applied pinning magnetic field exhibits a three sublattice feature, which is compatible with the 120 degrees Neel-ordered state realized in the limit of U -> 8. For U-c1 < U < U-c2, a response to the applied pinning magnetic field is comparable to that in the metallic phase with a relatively large spin correlation length, but showing neither valence bond nor chiral magnetic order, which therefore resembles gapless spin liquid. However, the spin structure factor for the intermediate phase exhibits the maximum at the K and K ' points in the momentum space, which is not compatible to spin liquid with a large spinon Fermi surface. The calculation also finds that the pairing correlation function monotonically decreases with increasing U and thus the superconductivity is unlikely in the intermediate phase.