Projected entangled pair states study of anisotropic-exchange magnets on the triangular lattice

The anisotropic-exchange spin-1/2 model on the 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 method, and compare it to the classical phase diagram. Besides two stripe-ordered phases, and the ${120}^{\ensuremath{\circ}}$ phase, there is also a multi-Q phase. We identify the multi-Q phase as a ${Z}_{2}$ vortex state. No quantum spin liquid state is found in the phase diagram, contrary to the previous density matrix renormalization group calculations.