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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.
We analyze a criterion which guarantees that the ground states of certain many body systems are stable under perturbations. Specifically, we consider PEPS, which are believed to provide an efficient description, based on local tensors, for the low en
Variational Monte Carlo studies employing projected entangled-pair states (PEPS) have recently shown that they can provide answers on long-standing questions such as the nature of the phases in the two-dimensional $J_1 - J_2$ model. The sampling in t
The recently developed stochastic gradient method combined with Monte Carlo sampling techniques [PRB {bf 95}, 195154 (2017)] offers a low scaling and accurate method to optimize the projected entangled pair states (PEPS). We extended this method to t
We present a scheme to perform an iterative variational optimization with infinite projected entangled-pair states (iPEPS), a tensor network ansatz for a two-dimensional wave function in the thermodynamic limit, to compute the ground state of a local
We investigate thermodynamic properties like specific heat $c_{V}$ and susceptibility $chi$ in anisotropic $J_1$-$J_2$ triangular quantum spin systems ($S=1/2$). As a universal tool we apply the finite temperature Lanczos method (FTLM) based on exact