MERA Study of Spatially Anisotropic Triangular Antiferromagnets

We report variational calculations for the ground states in the spatially anisotropic triangular antiferromagnets. The variational wave function is based on the tensor network with an entanglement renormalization [1]. The entanglement renormalization improves the ability of describing a quantum state. We construct a three-dimensional MERA tensor network for the triangular lattice models. The model in this study has two groups of the antiferromagnetic Heisenberg couplings on a triangular lattice: one on links along a lattice axis and the other on other links. $J_1$ and $J_2$ denote the coefficient of their couplings, respectively. We calculate the ground states of finite lattices ($N=114, 2166$) and an infinite lattice. We confirm a magnetic phase in the region of $0.7 < J_2/J_1 \le 1$. The magnetic structure is incommensurate, and the wave vector is not consistent with that of a classical model except for $J_1=J_2$.\\[4pt] [1] G. Vidal, Phys. Rev. Lett. 99, 220405 (2007).