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Spin-gap study of the spin-12\frac{1}{2} J1J_{1}--J2J_{2} model on the triangular lattice

Abstract

We use the coupled cluster method implemented at high orders of approximation to study the spin-12\frac{1}{2} J1J_{1}--J2J_{2} model on the triangular lattice with Heisenberg interactions between nearest-neighbour and next-nearest-neighbour pairs of spins, with coupling strengths J1>0J_{1}>0 and J2κJ1>0J_{2} \equiv \kappa J_{1} >0, respectively. In the window 0κ10 \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 κ<κ1c=0.060(10)\kappa < \kappa^{c}_{1} = 0.060(10) and κ>κ2c=0.165(5)\kappa > \kappa^{c}_{2} = 0.165(5), respectively. The spin-triplet gap is found to vanish over essentially the entire region κ1c<κ<κ2c\kappa^{c}_{1} < \kappa < \kappa^{c}_{2} of the intermediate phase

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