Fractional excitations in the Luttinger liquid

Abstract

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)

Charge and spin fractionalization beyond the Luttinger-liquid paradigm

“…Experimental evidences of its existence have been observed in quasi-1D organic conductors 3 , semiconductor quantum wires 4 , and quantum chains on semiconductor surfaces 5 . The LL theory also predicts the fractionalization of injected charge into two chiral modes (leftand right-going) [6][7][8][9][10] , a phenomenon recently confirmed experimentally 11 . Along the experimental advances also theoretical progress was recently achieved pertaining extensions beyond the LL limit by incorporating nonlinearity of the dispersion, leading to qualitative changes in the spectral function [12][13][14][15][16] and relaxation processes of 1D electronic systems 17 .…”

Charge fractionalization in nonchiral Luttinger systems

“…In fact, the theory predicts that nonchiral Luttinger liquids allow fractional states with irrational charges which correspond to exact eigenstates of the Luttinger model [8]; consult Appendix B.2. In addition, it should be emphasized that those anomalous charges must satisfy simple conservation laws.…”

“…Firstly, we introduce the chiral fields of nonchiral Luttinger liquids [1,8,9,11,15,27]. It is indeed convenient to distinguish the charge excitations propagating to the left (−) from the charge excitations propagating to the right (+).…”

“…We have used the definitions of the fluctuations in the charge (electron) density δρ = ρ − ρ 0 , where ρ 0 is the mean electron density, and of the current density in a Luttinger liquid for a spinful Luttinger liquid. The chiral densities are thus defined as [8]:…”

“…This fractional charge is not just a statistical average, but is predicted to be a definite property of the quantum mechanical state, subject in principle to verification by repeated measurements after a single tunneling event [8,9,10,11,12].…”