Frustrated Heisenberg antiferromagnet on the honeycomb lattice: Spin gap and low-energy parameters

We use the coupled cluster method implemented to high orders of approximation to investigate the frustrated spin-12J1-J2-J3 antiferromagnet on the honeycomb lattice with isotropic Heisenberg interactions of strength J1>0 between nearest-neighbor pairs, J2>0 between next-nearest neighbor pairs, and J3>0 between next-next-nearest-neighbor pairs of spins. In particular, we study both the ground-state (GS) and lowest-lying triplet excited-state properties in the case J3=J2≡κJ1, in the window 0≤κ≤1 of the frustration parameter, which includes the (tricritical) point of maximum classical frustration at κcl=12. We present GS results for the spin stiffness ρs and the zero-field uniform magnetic susceptibility χ, which complement our earlier results for the GS energy per spin E/N and staggered magnetization M to yield a complete set of accurate low-energy parameters for the model. Our results all point towards a phase diagram containing two quasiclassical antiferromagnetic phases, one with Néel order for κ<κc1, and the other with collinear striped order for κ>κc2. The results for both χ and the spin gap Δ provide compelling evidence for a disordered quantum paramagnetic phase that is gapped over a considerable portion of the intermediate region κc1<κ<κc2, especially close to the two quantum critical points at κc1 and κc2. Each of our fully independent sets of results for the low-energy parameters is consistent with the values κc1=0.45±0.02 and κc2=0.60±0.02, and with the transition at κc1 being of continuous (and hence probably of the deconfined) type and that at κc2 being of first-order type.