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

The ground-state (GS) phase diagram of the frustrated spin-s J(1)-J(2)-J(3) 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 J(1) > 0, J(2) > 0 and J(3) > 0, respectively). We specifically study the case J(3) = J(2) = kappa J(1), in the range 0 < kappa < 1 of the frustration parameter, which includes the point of maximum classical (s -> infinity) frustration, viz., the classical critical point at kappa(c1) = 1/2, which separates the Neel phase for kappa < kappa(c1) and the collinear striped AFM phase for kappa > kappa(c)]. 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 kappa(c)(s) which is slightly greater than kappa(c1) [e.g., kappa(c)(3/2) approximate to 0.53(1)] and which approaches it monotonically as s -> infinity. By contrast, for the case s = 1 the transition is split into two such that the stable GS phases are one with Neel AFM order for kappa < kappa(c1), = 0.485(5) and one with striped AFM order for n > kappa(c2) = 0.528(5), just as in the case s = 1/2 (for which kappa(c1) approximate to 0.47 and kappa(c2) approximate to 0.60). For both the s = 1/2 and s = 1 models the transition at kappa(c2) appears to be of first-order type, while that at kappa(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 kappa(c1) < kappa < kappa(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.