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 $\text{spin-}\frac{1}{2}{J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}$ antiferromagnet on the honeycomb lattice with isotropic Heisenberg interactions of strength ${J}_{1}g0$ between nearest-neighbor pairs, ${J}_{2}g0$ between next-nearest neighbor pairs, and ${J}_{3}g0$ 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 ${J}_{3}={J}_{2}\ensuremath{\equiv}\ensuremath{\kappa}{J}_{1}$, in the window $0\ensuremath{\le}\ensuremath{\kappa}\ensuremath{\le}1$ of the frustration parameter, which includes the (tricritical) point of maximum classical frustration at ${\ensuremath{\kappa}}_{\mathrm{cl}}=\frac{1}{2}$. We present GS results for the spin stiffness ${\ensuremath{\rho}}_{s}$ and the zero-field uniform magnetic susceptibility $\ensuremath{\chi}$, 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 $\ensuremath{\kappa}l{\ensuremath{\kappa}}_{{c}_{1}}$, and the other with collinear striped order for $\ensuremath{\kappa}g{\ensuremath{\kappa}}_{{c}_{2}}$. The results for both $\ensuremath{\chi}$ and the spin gap $\mathrm{\ensuremath{\Delta}}$ provide compelling evidence for a disordered quantum paramagnetic phase that is gapped over a considerable portion of the intermediate region ${\ensuremath{\kappa}}_{{c}_{1}}l\ensuremath{\kappa}l{\ensuremath{\kappa}}_{{c}_{2}}$, especially close to the two quantum critical points at ${\ensuremath{\kappa}}_{{c}_{1}}$ and ${\ensuremath{\kappa}}_{{c}_{2}}$. Each of our fully independent sets of results for the low-energy parameters is consistent with the values ${\ensuremath{\kappa}}_{{c}_{1}}=0.45\ifmmode\pm\else\textpm\fi{}0.02$ and ${\ensuremath{\kappa}}_{{c}_{2}}=0.60\ifmmode\pm\else\textpm\fi{}0.02$, and with the transition at ${\ensuremath{\kappa}}_{{c}_{1}}$ being of continuous (and hence probably of the deconfined) type and that at ${\ensuremath{\kappa}}_{{c}_{2}}$ being of first-order type.