Fractional excitations in the Luttinger liquid
K.-V. Pham, M. Gabay, Pascal Lederer
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 us to make contact with the 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 wave function is also given for that spinon state. Our construction of the spectroscopy based on fractional states leads to several unique 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 one-dimensional counterpart of the Laughlin fractional Quantum Hall effect 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 that we are able to describe.
arXiv:cond-mat/9909295•Physical review. B, Condensed matter•Jun 15, 2000•135 citations