Spinons and Holons - A Class of Simple-Models

In this paper, we discuss a class of quasi-one-dimensional models containing both spins and charge, which share the same generic solutions. In particular, we 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, we have successfully constructed a sufficiently simple representation for the 'spinon' excitation which allows us to calculate its dispersion using elementary methods. This is therefore a concrete example of a 'spinon' excitation for which explicit representation has been possible.