${\mathit{J}}_1$-${\mathit{J}}_2$ quantum Heisenberg antiferromagnet on the triangular lattice: A group-symmetry analysis of order by disorder

On the triangular lattice, for ${\mathit{J}}_2$/${\mathit{J}}_1$ between 1/8 and 1, the classical Heisenberg model with first- and second-neighbor interactions presents four-sublattice ordered ground states. Spin-wave calculations of Chubukov and Jolicoeur and Korshunov suggest that quantum fluctuations select amongst these states a collinear two-sublattice order. From theoretical requirements, we develop the full symmetry analysis of the low-lying levels of the spin-1/2 Hamiltonian in the hypotheses of either a four- or a two-sublattice order. We show on the exact spectra of periodic samples (N=12, 16, and 28) how quantum fluctuations select the collinear order from the four-sublattice order.