Spin-gap study of the spin-$\frac{1}{2}$ $J_1$--$J_2$ model on the triangular lattice

Abstract

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 $0\le \kappa \le 1$ we find that the 3-sublattice 120${}^{\circ }$ Néel-ordered and 2-sublattice 180${}^{\circ }$ stripe-ordered antiferromagnetic states form the stable ground-state phases in the regions $\kappa <{\kappa }_1^c=0.060(10)$ and $\kappa >{\kappa }_2^c=0.165(5)$, respectively. The spin-triplet gap is found to vanish over essentially the entire region ${\kappa }_1^c<\kappa <{\kappa }_2^c$ of the intermediate phase.