  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 Uc1 =
7.55 t and Uc2 = 9.65 t (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 < Uc1 implies that this phase
corresponds to a metallic phase. The local spin density induced by an applied
pinning magnetic field for U > Uc2 exhibits a three sublattice feature, which
is compatible with the Neel ordered state realized in the strong coupling
limit. For Uc1 < U < Uc2, a response to the applied pinning magnetic field is
comparable to that in the metallic phase but a relatively large spin
correlation length is found with neither valence bond nor chiral magnetic
order, suggesting a paramagnetic nature which resembles gapless spin liquid.
The calculation also finds that the pair- ing correlation function
monotonically decreases with increasing U and thus the superconductivity is
unlikely in the intermediate phase.

Strongly Correlated Electrons