Multimagnon bound states in the frustrated ferromagnetic one-dimensional chain

We study a one-dimensional Heisenberg chain with competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions in a magnetic field. Starting from the fully polarized high-field state, we calculate the dispersions of the lowest-lying n-magnon excitations and the saturation field $(n=2,3,4)$. We show that the lowest-lying excitations are always bound multimagnon states with a total momentum of π except for a small parameter range. We argue that Bose condensation of the bound n magnons leads to novel Tomonaga-Luttinger liquids with multipolar correlations; nematic- and triatic-ordered liquids correspond to $n=2$ and $n=3$.