We reconsider the spectrum of the Luttinger liquid (LL) usually understood in
terms of phonons (density fluctuations), and within the context of bosonization
we give an alternative representation in terms of fractional states. This
allows to make contact with Bethe Ansatz which predicts similar fractional
states. As an example we study the spinon operator in the absence of spin
rotational invariance and derive it from first principles: we find that it is
not a semion in general; a trial Jastrow wavefunction is also given for that
spinon state. Our construction of the new spectroscopy based on fractional
states leads to several new physical insights: in the low-energy limit, we find
that the $S_{z}=0$ continuum of gapless spin chains is due to pairs of
fractional quasiparticle-quasihole states which are the 1D counterpart of the
Laughlin FQHE quasiparticles. The holon operator for the Luttinger liquid with
spin is also derived. In the presence of a magnetic field, spin-charge
separation is not realized any longer in a LL: the holon and the spinon are
then replaced by new fractional states which we are able to describe.Comment: Revised version to appear in Physical Review B. 27 pages, 5 figures.
Expands cond-mat/9905020 (Eur.Phys.Journ.B 9, 573 (1999)
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.