  The ground-state phase diagram of the two-dimensional t-J model is
investigated in the context of the tensor network algorithm in terms of the
graded Projected Entangled-Pair State representation of the ground-state wave
functions. There is a line of phase separation between the Heisenberg
anti-ferromagnetic state without hole and a hole-rich state. For both J=0.4t
and J=0.8t, a systematic computation is performed to identify all the competing
ground states for various dopings. It is found that, besides a possible
Nagaoka's ferromagnetic state, the homogeneous regime consists of four
different phases: one phase with charge and spin density wave order coexisting
with a p_x (p_y)-wave superconducting state, one phase with the symmetry mixing
of d+s-wave superconductivity in the spin-singlet channel and p_x (p_y)-wave
superconductivity in the spin-triplet channel in the presence of an
anti-ferromagnetic background, one superconducting phase with extended s-wave
symmetry, and one superconducting phase with p_x (p_y)-wave symmetry in a
ferromagnetic background.
