$U(1)$-symmetric infinite projected entangled-pair state study of the spin-$1/2$ square $J_1-J_2$ 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 $J_1-J_2$ 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 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 $J_2/J_1<0.53$. For $0.53<J_2/J_1<0.61$, 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 $\xi \sim D^{1.2}$ and vanishing order parameters are consistent with a deconfined Néel-to-VBS transition at $J_2^{c_1}/J_1=0.530(5)$, where estimated critical anomalous exponents are ${\eta }_s\sim 0.6$ and ${\eta }_d\sim 1.9$ 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 $J_2^{c_2}/J_1=0.610(2)$ to the conventional Stripe phase. We compare our results with earlier DMRG and PEPS studies and suggest future directions for resolving remaining issues.

11 pages, 11 figures, sample source codes are available at https://github.com/rezah/ipeps

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