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

We use the coupled cluster method (CCM) to study the zero-temperature ground-state (GS) properties of a spin-1/2 $J_1$–$J_2$ Heisenberg antiferromagnet on a triangular lattice with competing nearest-neighbor and next-nearest-neighbor exchange couplings $J_1>0$ and $J_{2} \equiv \kappa J_{1}>0$,respectively,inthewindow$0 \leq \kappa < 1$. The classical version of the model has a single GS phase transition at ${\kappa }^{cl}=$1/8 in this window from a phase with 3-sublattice antiferromagnetic (AFM) 120${}^{\circ }$ N'{e}el order for $\kappa <{\kappa }^{cl}$ to an infinitely degenerate family of 4-sublattice AFM N'{e}el phases for $\kappa > \kappa^{cl}$. 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 $\kappa =0$ of the spin-1/2 model for the GS energy per spin, $E\mathrm{/}N=-0.5521(2)J_1$, and the GS magnetic order parameter, $M=0.198(5)$, which are among the best available. For the spin-1/2 $J_1$–$J_2$ model we find that the classical transition at $\kappa ={\kappa }^{cl}$ is split into two quantum phase transition at ${\kappa }_1^c=0.060(10)$ and ${\kappa }_2^c=0.165(5)$. The two quasiclassical AFM states (viz., the 120${}^{\circ }$ N'{e}el state and the striped state) are found to be the stable GS phases in the regime $\kappa < \kappa^{c}{1}$and$\kappa > \kappa^{c}{2}$, respectively, while in the intermediate regimes ${\kappa }_1^c<\kappa <{\kappa }_2^c$ the stable GS phase has no evident long-range magnetic order.