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 $J_{3}=J_{2} \equiv \kappa J_{1}$,inthewindow$0 \leq \kappa \leq 1$ of the frustration parameter, which includes the (tricritical) point of maximum classical frustration at ${\kappa }_{\mathrm{c}\mathrm{l}}=\frac{1}{2}$. We present GS results for the spin stiffness, ${\rho }_s$, and the zero-field uniform magnetic susceptibility, $\chi$, which complement our earlier results for the GS energy per spin, $E\mathrm{/}N$, 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 $\kappa <{\kappa }_{c_1}$, and the other with collinear striped order for $\kappa >{\kappa }_{c_2}$. The results for both $\chi$ and the spin gap $\mathrm{\Delta }$ provide compelling evidence for a quantum paramagnetic phase that is gapped over a considerable portion of the intermediate region $\kappa_{c_{1}} < \kappa < \kappa_{c_{2}}$, especially close to the two quantum critical points at ${\kappa }_{c_1}$ and ${\kappa }_{c_2}$. Each of our fully independent sets of results for the low-energy parameters is consistent with the values ${\kappa }_{c_1}=0.45\pm 0.02$ and ${\kappa }_{c_2}=0.60\pm 0.02$, and with the transition at ${\kappa }_{c_1}$ being of continuous (and probably of the deconfined) type and that at ${\kappa }_{c_2}$ being of first-order type.