Bound states and deconfined spinons in the dynamical structure factor of the J1-J2 spin-1 chain

Using a time-dependent density matrix renormalization group approach, we study the dynamical structure factor of the J1-J2 spin-1 chain. As J2 increases, the magnon mode develops incommensurability. The system undergoes a first-order transition at J2=0.76J1, and at that point, domain walls lead to a continuum of fractional quasiparticles or spinons. By studying small variations in J2 around the transition point, we observe the confinement of spinons into bound states in the spectral function and find a smooth evolution of the spectrum into magnon modes away from the phase transition. We employ the single-mode approximation to accurately account for the dispersion of the magnon mode away from the phase transition and describe the associated continua and bound states. We extend the single-mode approximation to describe the dispersion of a spinon at the phase transition point and obtain its dispersion throughout the Brillouin zone. This allows us to relate the incommensurability at and around the transition point to the competition between a negative nearest-neighbor hopping amplitude and a positive next-nearest-neighbor one for the domain wall.