Frustrated Heisenberg antiferromagnet on the honeycomb lattice with spin quantum number s ≥ 1

The ground-state (GS) phase diagram of the frustrated spin-s J₁-J₂-J₃ Heisenberg antiferromagnet on the honeycomb lattice is studied using the coupled cluster method implemented to high orders of approximation, for spin quantum numbers s = 1, 3/2, 2 , 5/2. The model has antiferromagnetic (AFM) nearest-neighbour, next-nearest-neighbour and next-next-nearest-neighbour exchange couplings (with strength J₁ > 0, J₂ > 0 and J₃ > 0, respectively). We specifically study the case J₃ = J₂ = κJ₁, in the range 0 < κ < 1 of the frustration parameter, which includes the point of maximum classical (s → ∞) frustration, viz., the classical critical point at κ_cl = 1/2, which separates the Neel phase for κ < κ_cl and the collinear striped AFM phase for κ > κ _cl. Results are presented for the GS energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. For all spins s > 3/2 we find a quantum phase diagram very similar to the classical one, with a direct first-order transition between the two collinear AFM states at a value κ_c(s) which is slightly greater than κ_cl [e.g., κ_c(3/2) ≈ 0.53(1)] and which approaches it monotonically as s → ∞. By contrast, for the case s = 1 the transition is split into two such that the stable GS phases are one with Néel AFM order for κ < κ_c1 = 0.485(5) and one with striped AFM order for κ > κ_c2 = 0.528(5), just as in the case s = 1/2 (for which κ_c1 ≈ 0.47 and κ_c2 ≈ 0.60). For both the s = 1/2 and s = 1 models the transition at κ_c2 appears to be of first-order type, while that at κ_c1 appears to be continuous. However, whereas in the s = 1/2 case the intermediate phase appears to have PVBC order over the entire range κ_c1 < κ < κ_c2, in the s = 1 case PVBC ordering either exists only over a very small part of the region or, more likely, is absent everywhere.