Quasiclassical magnetic order and its loss in a spin-1/2 Heisenberg antiferromagnet on a triangular lattice with competing bonds

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We use the coupled cluster method (CCM) to study the zero-temperature ground-state (GS) properties of a spin-1/2 J₁--J₂ Heisenberg antiferromagnet on a triangular lattice with competing nearest-neighbor and next-nearest-neighbor exchange couplings J₁>0 and J₂ ≡ κJ₁>0, respectively, in the window 0 ≤ κ< 1. The classical version of the model has a single GS phase transition at κcl=1/8 in this window from a phase with 3-sublattice antiferromagnetic (AFM) 120∘ Néel order for κ< κcl to an infinitely degenerate family of 4-sublattice AFM Néel phases for κ> κcl. This classical accidental degeneracy is lifted by quantum fluctuations, which favor a 2-sublattice AFM striped phase. For the quantum model we work directly in the thermodynamic limit of an infinite number of spins, with no consequent need for any finite-size scaling analysis of our results. We perform high-order CCM calculations within a well-controlled hierarchy of approximations, which we show how to extrapolate to the exact limit. In this way we find results for the case κ= 0 of the spin-1/2 model for the GS energy per spin, E/N=-0.5521(2)J₁, and the GS magnetic order parameter, M=0.198(5), which are among the best available. For the spin-1/2 J₁--J₂ model we find that the classical transition at κ=κcl is split into two quantum phase transition at κᶜ₁=0.060(10) and κᶜ₂=0.165(5). The two quasiclassical AFM states (viz., the 120∘ Néel state and the striped state) are found to be the stable GS phases in the regime κ< κᶜ₁ and κ> κᶜ₂, respectively, while in the intermediate regimes κᶜ₁ < κ< κᶜ₂ the stable GS phase has no evident long-range magnetic order.