Spin-i1/2 J_1- J_2 Heisenberg antiferromagnet on a square lattice:A plaquette renormalized tensor network study

摘要

We apply the plaquette renormalization scheme of tensor network states [Phys. Rev. E 83, 056703 (2011)] to study the spin-1/2 frustrated Heisenberg J_1-J_2 model on an L × L square lattice with L = 8, 16, and 32. By treating tensor elements as variational parameters, we obtain the ground states for different J_2/J_1 values, and investigate staggered magnetizations, nearest-neighbor spin-spin correlations, and plaquette order parameters. In addition to the well-known Neel order and collinear order at low and high J_2/J_1, we observe a plaquettelike order at J_2/J_1 ≈ 0.5. A continuous transition between the Neel order and the plaquettelike order near 7_2~(c1) ≈ 0.40J_1 is observed. The collinear order emerges at J_2~(c2) ≈ 0.62J_1 through a first-order phase transition.