## Abstract

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} = κJ_{1}, 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_{c}l [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.

Original language | English (US) |
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Article number | 012001 |

Journal | Journal of Physics: Conference Series |

Volume | 702 |

Issue number | 1 |

DOIs | |

State | Published - 2016 |

Event | 18th International Conference on Recent Progress in Many-Body Theories, MBT 2015 - Niagara Falls, United States Duration: Aug 16 2015 → Aug 21 2015 |