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arXiv:2609.25243

Extended symmetric quantum phase in a honeycomb Heisenberg model with sublattice-selective interactions

Nai Chao Hu, Xing-Yu Zhang, Yuchi He, Nick Bultinck

cond-mat.str-elquant-phSubmitted Sep 21, 2026• Announced Sep 23, 2026• 0 citations
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Abstract

Motivated by two-dimensional bilayer systems we numerically study an anti-ferromagnetic spin-$1/2$ Heisenberg model on the honeycomb lattice with a nearest-neighbour exchange coupling $J_1$, and a next-nearest-neighbour exchange coupling $J_2'$ for the B sublattice sites only. Using infinite Projected Entangled-Pair States (iPEPS), variational uniform matrix-product states on cylinders, and exact diagonalization, we find an extended symmetric regime $0.4\lesssim J'_2/J_1\lesssim0.6$, in which local observables show no magnetic, valence-bond, or chiral spin order. At $J'_2/J_1=0.5$, the PEPS correlation length grows systematically with bond dimension, and an inverse-correlation-length extrapolation favors a vanishing limit. We also find that various observables scale algebraically with the finite bond-dimension-induced correlation length, which points to a gapless spin liquid ground state. We propose a $\mathbb{Z}_2$ Dirac spin liquid parton state, with Dirac points that are protected by translation, time-reversal and three-fold rotation symmetry, as a promising candidate state to explain the numerical results. We also discuss the possibility that the symmetric ground state is a featureless, short-range entangled state with a small gap.

Comments
20 pages, 22 figures

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We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling J1>0{J}_{1}>0J1​>0 and frustrating next-nearest-neighbor coupling ${J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}>0$, using the coupled cluster method implemented to high orders of approximation, and based on model states with different forms of classical magnetic order. For each we calculate directly in the bulk thermodynamic limit both ground-state low-energy parameters (including the energy per spin, magnetic order parameter, spin stiffness coefficient, and zero-field uniform transverse magnetic susceptibility) and their generalized susceptibilities to various forms of valence-bond crystalline (VBC) order, as well as the energy gap to the lowest-lying spin-triplet excitation. In the range $0<\ensuremath{\kappa}<1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with two-sublattice N\'eel order for $\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{1}}=0.250(5)$, and another with four-sublattice N\'eel-II order for $\ensuremath{\kappa}>{\ensuremath{\kappa}}_{{c}_{2}}=0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range ${\ensuremath{\kappa}}_{{c}_{1}}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{c}^{i}=0.305(5)$ we find a gapless phase with no discernible magnetic order, which is a strong candidate for being a quantum spin liquid, while over the range ${\ensuremath{\kappa}}_{c}^{i}<\ensuremath{\kappa}<{\ensuremath{\kappa}}_{{c}_{2}}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.
We develop an improved variant of U(1)U(1)U(1)-symmetric infinite projected entangled-pair states (iPEPS) ansatz to investigate the ground-state phase diagram of the spin-1/21/21/2 square ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ 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)U(1)U(1)-symmetric iPEPS ansatz (for a fixed bond dimension D)D)D) set a better upper bound, improving previous tensor-network-based results. By studying the finite-DDD scaling of the magnetically order parameter, we find a N\'eel phase for J2/J1<0.53{J}_{2}/{J}_{1}<0.53J2​/J1​<0.53. For 0.53<J2/J1<0.610.53<{J}_{2}/{J}_{1}<0.610.53<J2​/J1​<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 $\ensuremath{\xi}\ensuremath{\sim}{D}^{1.2}$ and vanishing order parameters are consistent with a deconfined N\'eel-to-VBS transition at J2c1/J1=0.530(5){J}_{2}^{{c}_{1}}/{J}_{1}=0.530(5)J2c1​​/J1​=0.530(5), where estimated critical anomalous exponents are ${\ensuremath{\eta}}_{s}\ensuremath{\sim}0.6$ and ${\ensuremath{\eta}}_{d}\ensuremath{\sim}1.9$ for spin and dimer correlations, respectively. We show that the associated VBS order parameter monotonically increases with J2/J1{J}_{2}/{J}_{1}J2​/J1​ and finally a first-order quantum phase transition takes place at J2c2/J1=0.610(2){J}_{2}^{{c}_{2}}/{J}_{1}=0.610(2)J2c2​​/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.
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Investigation of the J1J_1J1​-J2J_2J2​ Heisenberg model on the triangular lattice: A study with projected entangled-pair states
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The U(1)U(1)U(1)-symmetric iPEPS study of the spin-1/21/21/2 square J1J_{1}J1​-J2J_{2}J2​ Heisenberg model
We develop an improved variant of U(1)U(1)U(1)-symmetric infinite projected entangled-pair states (iPEPS) ansatz to investigate the ground state phase diagram of the spin-1/21/21/2 square J1J_{1}J1​-J2J_{2}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)U(1)U(1)-symmetric iPEPS ansatz (for a fixed bond dimension DDD) set a better upper bound, improving previous tensor-network-based results. By studying N\'{e}el order parameter and correlation function in the large-DDD limit, we find that a deconfined quantum-critical point occurs at J2c1=0.530(5)J^{c_1}_{2}=0.530(5)J2c1​​=0.530(5), where the correlation length of the system diverges as ξ∼D1.2\xi \sim D^{1.2}ξ∼D1.2. The estimated critical anomalous exponents ηs=0.65(5)\eta_{s}=0.65(5)ηs​=0.65(5) and ηd=1.9(1)\eta_{d}=1.9(1)ηd​=1.9(1) for spin and dimer correlations respectively show strong deviation from those of the well-known J\mathcal{J}J-Q\mathcal{Q}Q model, suggesting possibly a different universality class. The pattern of local bond energy for the intermediate phase is compatible with the columnar valence bond solid (VBS) state, with a quite competitive variational ground-state energy in comparison with plaquette VBS one predicted by the density matrix renormalization group. We show that the associated VBS order parameter first monotonically increases with J2J_2J2​ and finally a first-order quantum phase transition takes place at J2c2=0.610(3)J^{c_2}_{2}=0.610(3)J2c2​​=0.610(3) to the conventional Stripe phase. We compare our results with earlier DMRG and PEPS studies and suggest future directions for resolving remaining issues.
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