  We revisit the unrestricted Hartree Fock study on the evolution of the ground
state of the Hubbard model on the triangular lattice with hole doping. At
half-filling, it is known that the ground state of the Hubbard model on
triangular lattice develops a 120 degree coplanar order at half-filling in the
strong interaction limit, i.e., in the spin 1/2 anti-ferromagnetic Heisenberg
model on the triangular lattice. The ground state property in the doped case is
still in controversy even though extensive studies were performed in the past.
Within Hartree Fock theory, we find that the 120 degree order persists from
zero doping to about 0.3 hole doping. At 1/3 hole doping, a three-sublattice
collinear order emerges in which the doped hole is concentrated on one of the
three sublattices with antiferromagnetic Neel order on the remaining two
sublattices, which forms a honeycomb lattice. Between the 120 degree order and
1/3 doping region, a phase separation occurs in which the 120 degree order
coexists with the collinear anti-ferromagnetic order in different region of the
system. The collinear phase extends from 1/3 doping to about 0.41 doping,
beyond which the ground state is paramagnetic with uniform electron density.
The phase diagram from Hartree Fock could provide guidance for the future study
of the doped Hubbard model on triangular lattice with more sophisticated
many-body approaches.
