Spin-12J1-J2Heisenberg antiferromagnet on a square lattice: A plaquette renormalized tensor network study

Abstract

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 $L\ifmmode\times\else\texttimes\fi{}L$ 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 N\'eel order and collinear order at low and high ${J}_{2}/{J}_{1}$, we observe a plaquettelike order at ${J}_{2}/{J}_{1}\ensuremath{\approx}0.5$. A continuous transition between the N\'eel order and the plaquettelike order near ${J}_{2}^{{c}_{1}}\ensuremath{\approx}0.40{J}_{1}$ is observed. The collinear order emerges at ${J}_{2}^{{c}_{2}}\ensuremath{\approx}0.62{J}_{1}$ through a first-order phase transition.