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 $\pi$ 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 $n=3$.

Figure 1

(Color online) Energy dispersions for the multimagnon bands at the saturation field. Thin lines denote the onset of the scattering continuum, and thick lines show $n$-magnon bound states where relevant. With decreasing $J_1∕J_2$, the lowest excitations change from commensurate $(k=\pi )$ two-magnon bound states, incommensurate $(k<\pi )$ two-magnon bound states, commensurate three-magnon bound states, to commensurate four-magnon bound states.

Figure 2

(Color online) Saturation field versus $J_1∕J_2$. The solid curve “$n$ magnon” shows the saturation field $h_s$ obtained from the numerical $n$-magnon solutions $(n=2,3,4)$, while the curves “1 magnon” and “2 magnon” denote $h_s$ calculated from Eqs. (4, 7), respectively. The inset shows the region where our saturation field deviates from the two-magnon solution and the saturation fields for each multimagnon excitation.

Figure 3

(Color online) Mean length $⟨{\sum }_i{r}_i⟩$ of the bound multimagnon states versus $J_1∕J_2$. The kinks in the curves appear when the total momentum of the $n$-magnon bound state changes between incommensurate (where $⟨{\sum }_i{r}_i⟩$ is larger) and commensurate $(k=\pi )$.