Spin-gap study of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$ model on the triangular lattice

We use the coupled cluster method implemented at high orders of approximation to study the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$ model on the triangular lattice with Heisenberg interactions between nearest-neighbour and next-nearest-neighbour pairs of spins, with coupling strengths $J_{1}>0$ and $J_{2} \equiv \kappa J_{1} >0$, respectively. In the window $0 \leq \kappa \leq 1$ we find that the 3-sublattice 120$^{\circ}$ N\'{e}el-ordered and 2-sublattice 180$^{\circ}$ stripe-ordered antiferromagnetic states form the stable ground-state phases in the regions $\kappa < \kappa^{c}_{1} = 0.060(10)$ and $\kappa > \kappa^{c}_{2} = 0.165(5)$, respectively. The spin-triplet gap is found to vanish over essentially the entire region $\kappa^{c}_{1} < \kappa < \kappa^{c}_{2}$ of the intermediate phase.