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It is well established that at low energies one-dimensional (1D) fermionicsystems are described by the Luttinger liquid (LL) theory, that predictsphenomena like spin-charge separation, and charge fractionalization into chiralmodes. Here we show through the time evolution of an electron injected into a1D t-J model, obtained with time-dependent density matrix renormalizationgroup, that a further fractionalization of both charge and spin takes placebeyond the hydrodynamic limit. Its dynamics can be understood at thesupersymmetric point (J=2t) in terms of the excitations of the Bethe-Ansatzsolution. Furthermore we show that fractionalization with similarcharacteristics extends to the whole region corresponding to a repulsive LL.

Charge and Spin Fractionalization Beyond the Luttinger Liquid Paradigm