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Ground-state phases of the spin-1 J1J_{1}--J2J_{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 J1>0J_{1}>0 and frustrating next-nearest-neighbor coupling J2κJ1>0J_{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<κ<10 < \kappa < 1 we find evidence for four distinct phases. Two of these are quasiclassical phases with antiferromagnetic long-range order, one with 2-sublattice N\'{e}el order for κ<κc1=0.250(5)\kappa < \kappa_{c_{1}} = 0.250(5), and another with 4-sublattice N\'{e}el-II order for κ>κc2=0.340(5)\kappa > \kappa_{c_{2}} = 0.340(5). Two different paramagnetic phases are found to exist in the intermediate region. Over the range κc1<κ<κci=0.305(5)\kappa_{c_{1}} < \kappa < \kappa^{i}_{c} = 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 κci<κ<κc2\kappa^{i}_{c} < \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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