© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Journal of Physics Condensed Matter

Spinons and holons: a class of simple models

S C Y Siak, M W Long

Published Aug 10, 1992• 0 citations

Abstract

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.

DOI: 10.1088/0953-8984/4/32/017

Related papers

Spinons and holons for the one-dimensional three-band Hubbard models of high-temperature superconductors.

Jamil Tahir‐Kheli, William A. Goddard

The one-dimensional three-band Hubbard Hamiltonian is shown to be equivalent to an effective Hamiltonian that has independent spinon and holon quasiparticle excitations plus a weak coupling of the two. The spinon description includes both copper sites and oxygen hole sites leading to a one-dimensional antiferromagnet incommensurate with the copper lattice. The holons are spinless noninteracting fermions in a simple cosine band. Because the oxygen sites are in the Hamiltonian, the quasiparticles are much simpler than in the exact solution of the t-J model for 2t = +/- J. If a similar description is correct for two dimensions, then the holons will attract in a p-wave potential.

Proceedings of the National Academy of Sciences•Nov 1, 1993•2 citations

Exact solution to a strongly coupled Hubbard model in one dimension for high- Tc superconductors

Jamil Tahir‐Kheli, William A. Goddard

A Hamiltonian for the motion of oxygen holes strongly coupled to the Cu spins in a one-dimensional (1D) Cu-O lattice is solved exactly for all dopings. This Hamiltonian retains the dominant O-hole hopping term, that is, spin-exchange hopping of the hole spin with the intervening Cu spin and neglects the weaker non-spin-exchange hopping term. The excitations naturally separate into two independent quasiparticles: spinons and holons. It is this Hamiltonian that should be taken as the correct zeroth-order Hamiltonian from which perturbation theory should be applied. We show that the spinon spectrum is the spectrum of the 1D antiferromagnet incommensurate with the Cu lattice and the holons are spinless noninteracting fermions in a cosine band. The Cu-Cu spin correlation in the ground state increases linearly with doping from antiferromagnetic (-0.443) at x=0 to ferromagnetic (\ensuremath{\approxeq}0.19) at x=1.

Physical review. B, Condensed matter•Jan 1, 1993•3 citations

GROUND-STATE PROPERTIES AND ELEMENTARY EXCITATIONS OF THE ONE-DIMENSIONAL HUBBARD MODEL

J. M. P. Carmelo, D. Baeriswyl

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.

International Journal of Modern Physics B•Oct 1, 1988•7 citations

Elementary objects of the 1D Hubbard model

J. M. P. Carmelo

Exotic elementary objects such as "holons" and "spinons", which are widely used in descriptions of correlated electrons in reduced spatial dimensions, were introduced from analysis of the excitation branches of one-dimensional (1D) models. The 1D Hubbard model with effective nearest-neighbor hopping integral t and on-site repulsion U is a prominent example. In the last twenty years a large number of angle-resolved photoemission spectroscopy experiments as well as electron energy-loss spectroscopic studies and high-resolution resonant inelastic X-ray experiments on several quasi-1D metals and quasi-1D Mott-Hubbard insulators have observed separate charge and spin spectral features, which have been identified with "holons" and "spinons". The elementary objects emerging within non-perturbative 1D correlated systems play now the same role in actual low-dimensional materials as Fermi-liquid quasiparticles in three-dimensional metals. The main goal of this paper is the review of representations of the 1D Hubbard model physics in terms of elementary objects whose configurations generate the energy eigenstates from the electron or hole vacuum. In addition, the relation to the holon and spinon representations is discussed and clarified.

arXiv:1211.5391•Nov 22, 2012•1 citation

Interaction among particles with fractionalized quantum numbers in one dimensional samples

Bogdan Andrei Bernevig, Domenico Giuliano, R. B. Laughlin

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.

arXiv:cond-mat/0301593•Jan 30, 2003•0 citations

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

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

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.

•Jan 1, 2003•0 citations

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.

The one-dimensional three-band Hubbard Hamiltonian is shown to be equivalent to an effective Hamiltonian that has independent spinon and holon quasiparticle excitations plus a weak coupling of the two. The spinon description includes both copper sites and oxygen hole sites leading to a one-dimensional antiferromagnet incommensurate with the copper lattice. The holons are spinless noninteracting fermions in a simple cosine band. Because the oxygen sites are in the Hamiltonian, the quasiparticles are much simpler than in the exact solution of the t-J model for 2t = +/- J. If a similar description is correct for two dimensions, then the holons will attract in a p-wave potential.

A Hamiltonian for the motion of oxygen holes strongly coupled to the Cu spins in a one-dimensional (1D) Cu-O lattice is solved exactly for all dopings. This Hamiltonian retains the dominant O-hole hopping term, that is, spin-exchange hopping of the hole spin with the intervening Cu spin and neglects the weaker non-spin-exchange hopping term. The excitations naturally separate into two independent quasiparticles: spinons and holons. It is this Hamiltonian that should be taken as the correct zeroth-order Hamiltonian from which perturbation theory should be applied. We show that the spinon spectrum is the spectrum of the 1D antiferromagnet incommensurate with the Cu lattice and the holons are spinless noninteracting fermions in a cosine band. The Cu-Cu spin correlation in the ground state increases linearly with doping from antiferromagnetic (-0.443) at x=0 to ferromagnetic (\ensuremath{\approxeq}0.19) at x=1.

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.

Exotic elementary objects such as "holons" and "spinons", which are widely used in descriptions of correlated electrons in reduced spatial dimensions, were introduced from analysis of the excitation branches of one-dimensional (1D) models. The 1D Hubbard model with effective nearest-neighbor hopping integral t and on-site repulsion U is a prominent example. In the last twenty years a large number of angle-resolved photoemission spectroscopy experiments as well as electron energy-loss spectroscopic studies and high-resolution resonant inelastic X-ray experiments on several quasi-1D metals and quasi-1D Mott-Hubbard insulators have observed separate charge and spin spectral features, which have been identified with "holons" and "spinons". The elementary objects emerging within non-perturbative 1D correlated systems play now the same role in actual low-dimensional materials as Fermi-liquid quasiparticles in three-dimensional metals. The main goal of this paper is the review of representations of the 1D Hubbard model physics in terms of elementary objects whose configurations generate the energy eigenstates from the electron or hole vacuum. In addition, the relation to the holon and spinon representations is discussed and clarified.

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.