The spin-$1/2$ $J_1-J_2$ Heisenberg antiferromagnet on a square lattice:a plaquette renormalized tensor network study

We apply the plaquette renormalization scheme of tensor network states [Phys. Rev. E, 83, 056703 (2011)] to study the spin-1/2 frustrated Heisenberg J1-J2 model on a L*L square lattice with L = 8, 16 and 32. By treating tensor elements as variational parameters, we obtain the ground states for di?erent J2/J1 values, and investigate the staggered magnetic order parameters, the nearest-neighbor spin-spin correlations and the plaquette order parameters. In addition to the well-known N?eel-order and collinear-order at low and high J2/J1, we observe a plaquette order at intermediate J2/J1. A continuous transition between the N\'eel order and the plaquette order near J2 = 0.40J1 is observed. The collinear order emerges at J2 = 0.62J1 through a fi?rst-order phase transition.