  We study the localization dynamics of a SU(2) fermionic wavepacket launched
in a (pseudo)random potential. We show that in the limit of strong
inter-component repulsions, the total wavepacket exhibits a boomerang-like
dynamics, returning near its initial position as expected for non-interacting
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 position. 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.
