A high-order study of the quantum critical behavior of a frustrated spin-12\frac{1}{2} antiferromagnet on a stacked honeycomb bilayer


We study a frustrated spin-12\frac{1}{2} J1J_{1}--J2J_{2}--J3J_{3}--J1J_{1}^{\perp} Heisenberg antiferromagnet on an AAAA-stacked bilayer honeycomb lattice. In each layer we consider nearest-neighbor (NN), next-nearest-neighbor, and next-next-nearest-neighbor antiferromagnetic (AFM) exchange couplings J1J_{1}, J2J_{2}, and J3J_{3}, respectively. The two layers are coupled with an AFM NN exchange coupling J1δJ1J_{1}^{\perp}\equiv\delta J_{1}. The model is studied for arbitrary values of δ\delta along the line J3=J2αJ1J_{3}=J_{2}\equiv\alpha J_{1} that includes the most highly frustrated point at α=12\alpha=\frac{1}{2}, where the classical ground state is macroscopically degenerate. The coupled cluster method is used at high orders of approximation to calculate the magnetic order parameter and the triplet spin gap. We are thereby able to give an accurate description of the quantum phase diagram of the model in the αδ\alpha\delta plane in the window 0α10 \leq \alpha \leq 1, 0δ10 \leq \delta \leq 1. This includes two AFM phases with N\'eel and striped order, and an intermediate gapped paramagnetic phase that exhibits various forms of valence-bond crystalline order. We obtain accurate estimations of the two phase boundaries, δ=δci(α)\delta = \delta_{c_{i}}(\alpha), or equivalently, α=αci(δ)\alpha = \alpha_{c_{i}}(\delta), with i=1i=1 (N\'eel) and 2 (striped). The two boundaries exhibit an "avoided crossing" behavior with both curves being reentrant

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