Excitations spin-charge decoupling

Spin and charge excitations are thus decoupled by coulombic interactions in the one-dimensional electron gas. However, the one-dimensional Fermion system is not a Fermi liquid, as indicated by the behavior of the momentum distribution function, which does not exhibit a Fermi step at kF and presents a single-particle density of states vanishing according to a power law singularity at EF. This is a Luttinger liquid [29] with... 

One drastic consequence of this model is the decoupling of charge and spin excitations, with the appearance of an energy gap along the energy axis. There is a split of the initial electronic band into two (U effect), or more (V effect) sub-bands, which are separated by a Hubbard gap (Fig. 3). The value of this gap has been calculated for a 1-D extended Hubbard model [26]. 

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