Elementary objects of the 1D Hubbard model

TL;DR

This paper reviews the elementary objects like holons and spinons in the 1D Hubbard model, explaining their role in describing correlated electrons and their experimental observations in low-dimensional materials.

Contribution

It provides a comprehensive review of the representations of the 1D Hubbard model in terms of elementary objects and clarifies their relation to holon and spinon descriptions.

Findings

Connection between elementary objects and energy eigenstates

Clarification of holon and spinon representations

Relevance to experimental observations in quasi-1D materials

Abstract

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.