What's the relation between SDW/CDW and spinon/holon in the one dimensional repulsive Hubbard model?

Question

As is well known, spin-charge separation occurs in the one dimensional repulsive Hubbard model. This phenomenon can be well understood by the Luttinger liquid theory, where spin density wave(SDW) and charge density wave(CDW) are described by separate bosonic fields and their group velocities are different when the Hubbard interaction is taken into account. In higher dimensions, instead of SDW/CDW, another set of objects, holon/spinon, seems to be the basics to describe spin charge separation in the literature. The different descriptions of spin charge separation in one dimension and higher dimensions seem to reflect two different scenarios: in one dimension the spin density and charge density of correlated electrons, which are essentially bosonic, fluctuate separately, while in higher dimensions the fractionalized parts of the electrons, e.g. holon and spinon, which may be bosonic or fermionic, can move separately. In some papers concerning the single particle spectral of one dimensional Hubbard model, the authors also talk about holon/spinon. So here are my questions: Are these two scenarios essentially different? Can we apply the second scenario(holon/spinon) to the one dimensional Hubbard model? If we can, what is the relation between SDW/CDW and holon/spinon?

This post imported from StackExchange Physics at 2017-08-29 09:31 (UTC), posted by SE-user Waltergu