A Creation Operator for Spinons in One Dimension

TL;DR

This paper introduces a creation operator for spinons in one-dimensional models, providing evidence it effectively creates single spinons and discussing its applications to various spin chain and Hubbard models.

Contribution

It defines a new creation operator for spinons and demonstrates its effectiveness in multiple one-dimensional quantum models.

Findings

Operator creates a nearly pure single spinon in the ISE model.

Numerical and analytical evidence supports the operator's effectiveness.

Potential applications to other spin chain models and the Hubbard model.

Abstract

We propose a definition for a creation operator for the spinon, the fractional statistics elementary excitation of the Haldane-Shastry model, and give numerical and analytical evidence that our operator creates a single spinon with nearly unit amplitude in the ISE model. We then discuss how the operator is useful in more general contexts such as studying the underlying spinons of other spin chain models, like the XXX- and XY-model, and of the one dimensional Hubbard model.