https://doi.org/10.1007/s100510050799
Wavefunctions for the Luttinger liquid
Laboratoire de Physique des Solides (associé au CNRS) , Université
Paris-Sud, 91405 Orsay Cedex, France
Corresponding author: a pham@lps.u-psud.fr
Received:
26
January
1999
Revised:
21
April
1999
Published online: 15 June 1999
Standard bosonization techniques lead to phonon-like excitations in a Luttinger liquid (LL), reflecting the absence of Landau quasiparticles in these systems. Yet in addition to the above excitations some LL are known to possess solitonic states carrying fractional quantum numbers (e.g. the spin 1/2 Heisenberg chain). We have reconsidered the zero modes in the low-energy spectrum of the Gaussian boson LL Hamiltonian both for fermionic and bosonic LL: in the spinless case we find that two elementary excitations carrying fractional quantum numbers allow to generate all the charge and current excited states of the LL. We explicitly compute the wavefunctions of these two objects and show that one of them can be identified with the 1D version of the Laughlin quasiparticle introduced in the context of the Fractional Quantum Hall effect. For bosons, the other quasiparticle corresponds to a spinon excitation. The eigenfunctions of Wen's chiral LL Hamiltonian are also derived: they are quite simply the one dimensional restrictions of the 2D bulk Laughlin wavefunctions.
PACS: 71.10.Pm – Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) / 71.27.+a – Strongly correlated electron systems; heavy fermions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999