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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-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$ antiferromagnet on the honeycomb lattice with isotropic Heisenberg interactions of strength $J_{1} > 0$ between nearest-neighbor pairs, $J_{2}>0$ between next-nearest-neighbor pairs, and $J_{3}>0$ between next-next-neareast-neighbor pairs of spins. In particular, we study both the ground-state (GS) and lowest-lying triplet excited-state properties in the case $J_{3}=J_{2} \equiv κJ_{1}$, in the window $0 \leq κ\leq 1$ of the frustration parameter, which includes the (tricritical) point of maximum classical frustration at $κ_{\rm cl} = \frac{1}{2}$. We present GS results for the spin stiffness, $ρ_{s}$, 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 $κ< κ_{c_{1}}$, and the other with collinear striped order for $κ> κ_{c_{2}}$. The results for both $χ$ and the spin gap $Δ$ provide compelling evidence for a quantum paramagnetic phase that is gapped over a considerable portion of the intermediate region $κ_{c_{1}} < κ< κ_{c_{2}}$, especially close to the two quantum critical points at $κ_{c_{1}}$ and $κ_{c_{2}}$. Each of our fully independent sets of results for the low-energy parameters is consistent with the values $κ_{c_{1}} = 0.45 \pm 0.02$ and $κ_{c_{2}} = 0.60 \pm 0.02$, and with the transition at $κ_{c_{1}}$ being of continuous (and probably of the deconfined) type and that at $κ_{c_{2}}$ being of first-order type.