Multi-magnon bound states in the frustrated ferromagnetic 1D chain

We study a one-dimensional Heisenberg chain with competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest neighbor interactions in 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 multi-magnon states with a total momentum of $\pi$ except for a small parameter range. We argue that bose condensation of the bound $n$ magnons leads to novel Tomonaga-Luttinger liquids with multi-polar correlations; nematic and triatic ordered liquids correspond to n=2 and n=3.