On the Hubbard Model in the Limit of Vanishing Interaction

TL;DR

This paper investigates how the one-dimensional Hubbard model's particle-like excitations relate to free fermions as interaction strength approaches zero, focusing on finite size spectra and degeneracy lifting.

Contribution

It provides a detailed analysis of the correspondence between Hubbard model excitations and free fermions in the zero-interaction limit, especially considering degeneracies at zero magnetic field.

Findings

Established the connection between holons/spinons and free fermions at vanishing interaction.

Analyzed the finite size spectrum using Bethe Ansatz techniques.

Identified how interaction lifts degeneracies in excitation bands.

Abstract

We address the question how a correspondence between the particle like excitations in the one dimensional Hubbard model (i.e. ``holons'' and ``spinons'') and the free fermionic picture can be established in the limit of vanishing interaction by studying the finite size spectrum in the framework of the Bethe Ansatz. Special attention has to be paid to the case of a vanishing magnetic field where the two bands of excitations in either description are degenerate. The interaction lifts this degeneracy.