to -12pt [-12pt]to 16ptRapid Note Wavefunctions for the Luttinger liquid |
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Authors: | K-V Pham M Gabay P Lederer |
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Institution: | (1) Laboratoire de Physique des Solides (associé au CNRS), Université Paris-Sud, 91405 Orsay Cedex, France, FR |
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Abstract: | 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.
Received 26 January 1999 and Received in final form 21 April 1999 |
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Keywords: | PACS 71 10 Pm Fermions in reduced dimensions (anyons composite fermions Luttinger liquid etc ) - 71 27 +a Strongly correlated electron systems heavy fermions |
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