Charge and Spin Fractionalization Beyond the Luttinger Liquid Paradigm

TL;DR

This paper demonstrates that charge and spin fractionalization in one-dimensional fermionic systems extend beyond the traditional Luttinger liquid description, revealing new fractionalization phenomena through time-dependent simulations and Bethe-Ansatz analysis.

Contribution

It uncovers additional fractionalization effects in 1D systems beyond the Luttinger liquid paradigm, using numerical and analytical methods at the supersymmetric point and in the repulsive LL regime.

Findings

Charge and spin fractionalization beyond hydrodynamic limit.

Fractionalization dynamics understood via Bethe-Ansatz at supersymmetric point.

Similar fractionalization features observed in the repulsive LL regime.

Abstract

It is well established that at low energies one-dimensional (1D) fermionic systems are described by the Luttinger liquid (LL) theory, that predicts phenomena like spin-charge separation, and charge fractionalization into chiral modes. Here we show through the time evolution of an electron injected into a 1D t-J model, obtained with time-dependent density matrix renormalization group, that a further fractionalization of both charge and spin takes place beyond the hydrodynamic limit. Its dynamics can be understood at the supersymmetric point (J=2t) in terms of the excitations of the Bethe-Ansatz solution. Furthermore we show that fractionalization with similar characteristics extends to the whole region corresponding to a repulsive LL.