Collinear antiferromagnetic phases of a frustrated spin-12\frac{1}{2} J1J_{1}--J2J_{2}--J1J_{1}^{\perp} Heisenberg model on an AAAA-stacked bilayer honeycomb lattice


The zero-temperature quantum phase diagram of the spin-12\frac{1}{2} J1J_{1}--J2J_{2}--J1J_{1}^{\perp} model on an AAAA-stacked bilayer honeycomb lattice is investigated using the coupled cluster method (CCM). The model comprises two monolayers in each of which the spins, residing on honeycomb-lattice sites, interact via both nearest-neighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg exchange iteractions, with respective strengths J1>0J_{1} > 0 and J2κJ1>0J_{2} \equiv \kappa J_{1}>0. The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength J1δJ1J_{1}^{\perp} \equiv \delta J_{1}. The complete phase boundaries of two quasiclassical collinear AFM phases, namely the N\'{e}el and N\'{e}el-II phases, are calculated in the κδ\kappa \delta half-plane with κ>0\kappa > 0. Whereas on each monolayer in the N\'{e}el state all NN pairs of spins are antiparallel, in the N\'{e}el-II state NN pairs of spins on zigzag chains along one of the three equivalent honeycomb-lattice directions are antiparallel, while NN interchain spins are parallel. We calculate directly in the thermodynamic (infinite-lattice) limit both the magnetic order parameter MM and the excitation energy Δ\Delta from the sTz=0s^{z}_{T}=0 ground state to the lowest-lying sTz=1|s^{z}_{T}|=1 excited state (where sTzs^{z}_{T} is the total zz component of spin for the system as a whole, and where the collinear ordering lies along the zz direction) for both quasiclassical states used (separately) as the CCM model state, on top of which the multispin quantum correlations are then calculated to high orders (n10n \leq 10) in a systematic series of approximations involving nn-spin clusters. The sole approximation made is then to extrapolate the sequences of nnth-order results for MM and Δ\Delta to the exact limit, nn \to \infty

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