U(1)-symmetric infinite projected entangled-pair states study of the spin-1/2 square J(1)-J(2) Heisenberg model

摘要

We develop an improved variant of U(1)-symmetric infinite projected entangled-pair states (iPEPS) ansatz to investigate the ground-state phase diagram of the spin-1/2 square J(1)-J(2) Heisenberg model. In order to improve the accuracy of the ansatz, we discuss a simple strategy to select automatically relevant symmetric sectors and also introduce an optimization method to treat second-neighbor interactions more efficiently. We show that variational ground-state energies of the model obtained by the U(1)-symmetric iPEPS ansatz (for a fixed bond dimensionD) set a better upper bound, improving previous tensor-network-based results. By studying the finite-D scaling of the magnetically order parameter, we find a Neel phase for J(2)/J(1) 0.53. For 0.53 J(2)/J(1) 0.61, a nonmagnetic columnar valence bond solid (VBS) state is established as observed by the pattern of local bond energy. The divergent behavior of correlation length xi similar to D-1.2 and vanishing order parameters are consistent with a deconfined Neel-to-VBS transition at J(2)(c1) / J(1) = 0.530(5), where estimated critical anomalous exponents are eta(s) similar to 0.6 and eta(d) similar to 1.9 for spin and dimer correlations, respectively. We show that the associated VBS order parameter monotonically increases with J(2)/J(1) and finally a first-order quantum phase transition takes place at J(2)(c2) / J(1) = 0.610(2) to the conventional Stripe phase. We compare our results with earlier DMRG and PEPS studies and suggest future directions for resolving remaining issues.