U(1) -symmetric infinite projected entangled-pair states study of the spin-1/2 square J1−J2 Heisenberg model

Abstract

We develop an improved variant of U (1)-symmetric infinite projected entangled-pair state (iPEPS) ansatz to investigate the ground state phase diagram of the spin-1/2 square J1 − J2 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 dimension D) 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 Néel phase for J2/J1 < 0.53. For 0.53 < J2/J1 < 0.61, a non-magnetic columnar valence bond solid (VBS) state is established as observed by the pattern of local bond energy. The divergent behavior of correlation length ξ ∼ D 1.2 and vanishing order parameters are consistent with a deconfined Néel-to-VBS transition at J c 1 2 /J1 = 0.530(5), where estimated critical anomalous exponents are ηs ∼ 0.6 and η d ∼ 1.9 for spin and dimer correlations respectively. We show that the associated VBS order parameter monotonically increases with J2/J1 and finally a first-order quantum phase transition takes place at J c 2 2 /J1 = 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.

Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice

“…Recently, DMRG simulations of Wang and Sandvik using level spectroscopy [31] also indicate that the QD is formed by a gapless spin liquid phase (for 0.46 < J 2 < 0.52) and a VBC (for 0.52 < J 2 < 0.62). In contrast, other recent computations using U(1)-symmetric (infinite size) Projected Entangled Pair States (PEPS) [32] suggest a columnar VBC (for 0.53 < J 2 < 0.61) separated from the conventional Néel phase by a deconfined critical point [33], in qualitative agreement with a previous finite size PEPS computation [34]. Despite such recent progress, the exact nature of the QD phase remains still unclear.…”

“…. ) as suggested by large-N theories [67], series expansions [68,69] or numerical work [21,22,24,31,32]. In fact, Lanczos ED of small clusters (see Appendix (B) for details) suggests that the tendency to realize a VBC is maximum at J 2 0.55, although the VBC order parameter should be quite small, and probably very hard to detect directly.…”

Comment on “Gapless spin liquid ground state of the spin- 12 J1−J2 Heisenberg model on square lattices”

“…[1]. Judging from other recent calculations with a variety of methods [2][3][4][5], we expect VBS order in a narrow range of coupling ratios g = J 2 /J 1 (roughly for g ∈ 0.52, 0.61]). According to the same calculations, a gapless spin liquid may exist for slightly smaller values of g (roughly for g ∈ 0.45, 0.52]).…”

“…argued that there is a gapless spin liquid phase in the ground state of the S = 1/2 frustrated square-lattice J 1 -J 2 Heisenberg model for g = J 2 /J 1 ∈ [0.42, 0.6]. At variance with other recent works [2][3][4][5], they found no spontaneously dimerized valence-bond-solid (VBS) phase within this range of coupling ratios (where other works have roughly placed the VBS at g ∈ [0.52 − 0.61]). They reached their conclusions based on the method of Monte Carlo sampling of gradient-optimized tensor network states [6][7][8], which they have further refined for the specific case of a tensor network of the Projected Entangled Pair State (PEPS) type.…”

Translation constraints on quantum phases with twisted boundary conditions

“…The nature of this phase has long been discussed and is still controversial. In fact, there are many proposals for that phase such as the gapped spin-liquid phase [21,22], the gapless spin-liquid phase [23][24][25][26][27] and a columner valencebond-crystal phase [28].…”