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Interaction among particles with fractionalized quantum numbers in one-dimensional samples

Bernevig B. A, R. B. Laughlin, Domenico Giuliano

Published Jan 1, 2003• 0 citations
Publisher

Abstract

The elementary excitations of strongly correlated one-dimensional electronic systems - spinons and holons - are discussed in an exact solution of the Haldane-Shastry and Kuramoto-Yokoyama model. We derive and exactly solve the equation of motion both for the two-spinon wavefunction and for the one-spinon, one-holon wavefunction. By solving the equations of motion we find the spinon-spinon and spinon-holon interaction to be a short-range attraction. The physical consequences of such an attraction on the spin-form factor and on the hole-spectral function are also worked out.

DOI
10.3254/978-1-61499-007-9-375

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Interaction among particles with fractionalized quantum numbers in one dimensional samples

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The elementary excitations of strongly correlated one-dimensional electronic systems - spinons and holons - are discussed in an exact solution of the Haldane-Shastry and Kuramoto-Yokoyama model. We derive and exactly solve the equation of motion both for the two-spinon wavefunction and for the one-spinon, one-holon wavefunction. By solving the equations of motion we find the spinon-spinon and spinon-holon interaction to be a short-range attraction. The physical consequences of such an attraction on the spin-form factor and on the hole-spectral function are also worked out.
The elementary excitations of strongly correlated one-dimensional electronic systems - spinons and holons - are discussed in an exact solution of the Haldane-Shastry and Kuramoto-Yokoyama model. We derive and exactly solve the equation of motion both for the two-spinon wavefunction and for the one-spinon, one-holon wavefunction. By solving the equations of motion we find the spinon-spinon and spinon-holon interaction to be a short-range attraction. The physical consequences of such an attraction on the spin-form factor and on the hole-spectral function are also worked out.
By deriving and studying the coordinate representation for the one-spinon one-holon wave function we show that spinons and holons in the supersymmetric $t\ensuremath{-}J$ model with 1/r2{1/r}^{2}1/r2 interaction attract each other. The interaction causes a probability enhancement in the one-spinon one-holon wave function at short separation between the particles. We express the hole spectral function for a finite lattice in terms of the probability enhancement, given by the one-spinon one-holon wave function at zero separation. In the thermodynamic limit, the spinon-holon attraction turns into the square-root divergence in the hole spectral function.
The ground state of the one-dimensional Hubbard Hamiltonian is discussed on the basis of the Bethe ansatz solution of Lieb and Wu. A simple analytical representation of the distribution functions for charge and spin degrees of freedom is derived. The elementary excitations are associated with electron-hole pairs of two pseudo-fermion systems, one for the charge, the other for the magnetic excitations. Spinons and holons correspond to ground state configurations of odd-numbered rings. It is argued that holons will form bound pairs in weakly coupled chains.
In this paper, the authors discuss a class of quasi-one-dimensional models containing both spins and charge, which share the same generic solutions. In particular, they concentrate on a Heisenberg model of a topologically frustrated antiferromagnet, and a d-p model for oxygen hole hopping in a subgeometry of the copper-oxygen plane of the perovskite superconductors. The outstanding feature of these models lies in the simplicity of their solutions: their ground states are exact and contain uncorrelated, short-ranged singlet pairs. Excitations in these models fall into two distinct classes, namely, spin-1/2 chargeless domain-wall excitations or 'spinons', together with their conjugate excitations, which take the form of spin-1/2 chargeless 'antispinon' domain walls in the Heisenberg model, and spinless charge+e hole excitations or 'holons' in the d-p model. In the case of the Heisenberg model, the authors have successfully constructed a sufficiently simple representation for the 'spinon' excitation which allows them to calculate its dispersion using elementary methods. This is therefore a concrete example of a 'spinon' excitation for which explicit representation has been possible.
While the Bethe ansatz solution of the Haldane-Shastry model appears to suggest that the spinons represent a free gas of half-fermions Bernevig, Giuliano, and Laughlin (BGL) [Phys. Rev. Lett. 86, 3392 (2001); Phys. Rev. B 64, 24425 (2001)] have concluded recently that there is an attractive interaction between spinons. We argue that the dressed scattering matrix obtained with the asymptotic Bethe ansatz is to be interpreted as the true and physical scattering matrix of the excitations, and hence, that the result by BGL is inconsistent with an earlier result by Essler [Phys. Rev. B 51, 13357 (1995)]. We critically reexamine the analysis of BGL, and conclude that there is no interaction between spinons or spinons and holons in the Haldane-Shastry model.