Spin-charge separation in the quantum boomerang effect

We study the localization dynamics of a SU(2) fermionic wave packet launched in a (pseudo)random potential. We show that, in the limit of strong intercomponent repulsions, the total wave packet exhibits a boomeranglike dynamics, returning to near its initial position as expected for noninteracting particles, while separately each spin-component does not. This spin-charge separation effect occurs both in the infinite repulsive limit and at finite interactions. At infinite interactions, the system is integrable and thermalization cannot occur: the two spin-components push each other during the dynamics and their centers of mass stop further from each other than their initial positions. At finite interactions, integrability is broken, the two spin-components oscillate and mix, with their center-of-mass positions converging very slowly to the center of mass of the whole system. This is a signature that the final localized state is a fully spin-mixed thermalized state.