Spinons and helimagnons in the frustrated Heisenberg chain

Abstract

We investigate the dynamical spin structure factor $S(q,\ensuremath{\omega})$ for the Heisenberg chain with ferromagnetic nearest-neighbor (${J}_{1}<0$) and antiferromagnetic next-nearest-neighbor (${J}_{2}>0$) exchange using bosonization and a time-dependent density-matrix renormalization group algorithm. For $|{J}_{1}|\ensuremath{\ll}{J}_{2}$ and low energies we analytically find and numerically confirm two spinon branches with different velocities and different spectral weights. Following the evolution of $S(q,\ensuremath{\omega})$ with decreasing ${J}_{1}/{J}_{2}$, we find that helimagnons develop at high energies just before entering the ferromagnetic phase. Furthermore, we show that a recent interpretation of neutron-scattering data for LiCuVO${}_{4}$ in terms of two weakly coupled antiferromagnetic chains ($|{J}_{1}|\ensuremath{\ll}{J}_{2}$) is not viable. We demonstrate that the data are instead fully consistent with a dominant ferromagnetic coupling, ${J}_{1}/{J}_{2}\ensuremath{\approx}\ensuremath{-}2$.