Collinear antiferromagnetic phases of a frustrated spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ Heisenberg model on an $AA$-stacked bilayer honeycomb lattice

Abstract

The zero-temperature quantum phase diagram of the spin-$\frac{1}{2}$ $J_1$--$J_2$--$J_1^{\perp }$ model on an $AA$-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 $J_1>0$ and $J_2\equiv \kappa J_1>0$. The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength $J_1^{\perp }\equiv \delta J_1$. The complete phase boundaries of two quasiclassical collinear AFM phases, namely the Néel and Néel-II phases, are calculated in the $\kappa \delta$ half-plane with $\kappa >0$. Whereas on each monolayer in the Néel state all NN pairs of spins are antiparallel, in the Néel-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 $M$ and the excitation energy $\Delta$ from the $s_T^z=0$ ground state to the lowest-lying $|s_T^z|=1$ excited state (where $s_T^z$ is the total $z$ component of spin for the system as a whole, and where the collinear ordering lies along the $z$ 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 ($n\le 10$) in a systematic series of approximations involving $n$-spin clusters. The sole approximation made is then to extrapolate the sequences of $n$th-order results for $M$ and $\Delta$ to the exact limit, $n\to \infty$.

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Cited by in corpus (2)

• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_1$--$J_2$--$J_1^{\perp }$ model
• 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