  We investigate the quantum phase diagram of t-J model on triangular lattice
at 1/2 doping with various lattice sizes by using a combination of density
matrix renormalization group (DMRG), variational Monte Carlo and quantum field
theories. To sharply distinguish different phases, we calculated the symmetry
quantum numbers of the ground state wave functions, and the results are further
confirmed by studying correlation functions. Our results show there is a first
order phase transition from ferromagnetism to d+id superconductivity, with the
transition taking place at $J/t=0.4\pm0.2$.
