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, in the window $0 \leq \kappa < 1$. 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, $E/N=-0.5521(2)J_{1}$, 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 $\kappa^{c}_{1}=0.060(10)$ and $\kappa^{c}_{2}=0.165(5)$. 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 $\kappa^{c}_{1} < \kappa < \kappa^{c}_{2}$ the stable GS phase has no evident long-range magnetic order.