  The anisotropic-exchange spin-1/2 model on a triangular lattice has been used
to describe the rare-earth chalcogenides, which may have exotic ground states.
We investigate the quantum phase diagram of the model by using the projected
entangled pair state (PEPS) method, and compare it to the classical phase
diagram. Besides two stripe-ordered phase, and the 120$^\circ$ state, there is
also a multi-\textbf{Q} phase. We identify the multi-\textbf{Q} phase as a
$Z_{2}$ vortex state. No quantum spin liquid state is found in the phase
diagram, contrary to the previous DMRG calculations.
