Ground-state phases of the spin-1 $J_1$--$J_2$ Heisenberg antiferromagnet on the honeycomb lattice

Abstract

We study the zero-temperature quantum phase diagram of a spin-1 Heisenberg antiferromagnet on the honeycomb lattice with both nearest-neighbor exchange coupling $J_1>0$ and frustrating next-nearest-neighbor coupling $J_2\equiv \kappa J_1>0$, 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 $0<\kappa <1$ we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with 2-sublattice Néel order for $\kappa <{\kappa }_{c_1}=0.250(5)$, and another with 4-sublattice Néel-II order for $\kappa >{\kappa }_{c_2}=0.340(5)$. Two different paramagnetic phases are found to exist in the intermediate region. Over the range ${\kappa }_{c_1}<\kappa <{\kappa }_c^i=0.305(5)$ 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 ${\kappa }_c^i<\kappa <{\kappa }_{c_2}$ we find a gapped phase, which is most likely a lattice nematic with staggered dimer VBC order that breaks the lattice rotational symmetry.

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• Polarized-neutron investigation of magnetic ordering and spin dynamics in BaCo${}_2$(AsO${}_4$)${}_2$ frustrated honeycomb-lattice magnet
• Role of quantum fluctuations on spin liquids and ordered phases in the Heisenberg model on the honeycomb lattice
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• A high-order study of the quantum critical behavior of a frustrated spin-$\frac{1}{2}$ antiferromagnet on a stacked honeycomb bilayer
• Intertwining SU($N$) symmetry and frustration on a honeycomb lattice
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• Quantum phase diagram of $J_1-J_2$ Heisenberg $S=1/2$ antiferromagnet in honeycomb lattice: a modified spin wave study
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• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_1$--$J_2$--$J_1^{\perp }$ model