High-order study of the quantum critical behavior of a frustrated spin-½ antiferromagnet on a stacked honeycomb bilayer

We study a frustrated spin-½ J₁-J₂-J₃-J₁^⊥ Heisenberg antiferromagnet on an AA-stacked bilayer honeycomb lattice.  In each layer we consider nearest-neighbor (NN), next-nearest-neighbor, and next-next-nearest-neighbor
antiferromagnetic (AFM) exchange couplings J₁, J₂, and J₃, respectively.  The two layers are coupled with an AFM NNexchange coupling J₁^⊥≡ δ J₁. The model is studied for arbitrary values of δ along the line J₃ = J₂ ≡ α J₁ that includes the most highly frustrated point at α = ½, 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 plane in the window 0 ≤ α ≤ 1, 0 ≤ δ ≤ 1.  This includes two AFM phases with Néel 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 = δ_ci (α), or equivalently, α = α_ci (δ), with i = 1 (Néel) and 2 (striped).  The two boundaries exhibit an “avoided crossing” behavior with both curves being re-entrant.  Thus, in this αδ window, Néel order exists only for values of δ in the range δ_c1^<(α) < δ < δ_c1^>(α), with δ_c1^<(α) = 0 for α < α_c1(0) ≈ 0.46(2) and δ_c1^<(α) > 0 for α_c1(0) < α < α₁^> ≈ 0.49(1), and striped order similarly exists only for values of δ in the range δ_c2^<(α) < δ < δ_c2^>(α), with δ_c2^<(α) = 0 for
α > α_c2(0) ≈ 0.600(5) and δ_c2^<(α) > 0 for α_c2(0) > α > α₂^< ≈ 0.56(1).