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-1/2J₁-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=1/2. 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 N\'eel order for κ<κ_c₁, and the other with collinear striped order for κ>κ_c₂. 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 κ_c₁<κ<κ_c₂, especially close to the two quantum critical points at κ_c₁ and κ_c₂. Each of our fully independent sets of results for the low-energy parameters is consistent with the values κ_c₁=0.45±0.02 and κ_c₂=0.60±0.02, and with the transition at κ_c₁ being of continuous (and hence probably of the deconfined) type and that at κ_c₂ being of first-order type.