The phase diagram of spin-1/2 square J₁-J₂ Heisenberg model: U(1)-symmetric infinite PEPS study

The tensor-network states have shown to be quite promising in studying the frustrated systems. Specifically, infinite projected entangled-pair state (iPEPS) anstaz, a generalization of powerful DMRG, could efficiently address the low-lying excited states of such systems and provide quite competitive variational energy. In this talk, we aim to introduce an "improved" U(1)-symmetric iPEPS anstaz and study phase diagram of the canonical spin-1/2 square J₁-J₂ Heisenberg model. We discuss a simple strategy to selects automatically relevant symmetric sectors without losing accuracy and also discuss an improved optimization method. We show variational ground-state energies of the model set better upper bound on the true energy, improving previous tensor-network-based results. By studying magnetization parameter and correlation functions, we find a direct Néel-to-VBS transition at J₂=0.53. The estimated critical anomalous exponents η_s=0.65(5) and η_d=1.9(1) show strong deviation from those of the well-known J-Q models, suggesting possibly different universality class. We compare our results with earlier DMRG and PEPS studies and suggest future directions for resolving remaining issues.