Spin-charge separation in strongly interacting multicomponent few-body systems

The effect of spin-charge separation is known to happen in one-dimensional many-body systems in the presence of interactions between particles. In a few-body regime, however, little is known about this phenomenon. To address this problem, we describe the time-evolution of a small system of strongly interacting fermions with SU(N) symmetry after a sudden change in the trapping geometry. The presence of strong contact interactions allows for a mapping between a multicomponent repulsive gas and an effective spin chain, where the internal degrees of freedom of the atoms play the role of different spin projections. This model captures the dynamical behavior of the system by taking into account a set of time-dependent exchange coefficients, which are determined by the instantaneous spatial densities of the system. We show how changing the trapping potential influences the spatial distribution of each atomic species in the ground state of the spin chain. We then obtain the dynamics of the spin densities after a sudden change in the trap. Even at the few-body level, the excitation spectrum for this quantity presents clear separate signatures of both spin and charge dynamics. Moreover, as the number of internal components is increased, we show that the spin excitations vanish, and the dynamics can be predicted by the excitation frequencies expected for a gas of impenetrable bosons. Additionally, we include the description of the dynamics under the same quench protocol in a system where SU(N) symmetry is broken.