Wavefunctions for the Luttinger liquid

TL;DR

This paper explores the wavefunctions of the Luttinger liquid, revealing fractional quantum number excitations and connecting them to Laughlin quasiparticles and spinons, enhancing understanding of low-energy excitations in 1D systems.

Contribution

It explicitly constructs wavefunctions for fractional excitations in Luttinger liquids, linking them to Laughlin quasiparticles and spinons, and extends the analysis to chiral LLs.

Findings

Identified two elementary fractional excitations generating all charge and current states.

Derived wavefunctions for these excitations, linking one to Laughlin quasiparticles.

Connected eigenfunctions of chiral LL to 1D restrictions of Laughlin wavefunctions.

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.