Conservation laws and bosonization in integrable Luttinger liquids

TL;DR

This paper introduces a bosonic operator algebra to describe the Luttinger-liquid behavior in integrable models like the Hubbard chain, unifying and extending previous results across all parameter regimes.

Contribution

It develops a bosonic operator framework for Bethe ansatz solvable models, applicable to all parameters, and clarifies the charge-spin separation and pseudoparticle concepts.

Findings

Bosonic algebra describes Luttinger liquids in integrable models.

Unified treatment of Hubbard chain for all U, density, and magnetization.

Clarification of pseudoparticle and charge-spin separation concepts.

Abstract

We examine and explain the Luttinger-liquid character of models solvable by the Bethe ansatz by introducing a suitable bosonic operator algebra. In the case of the Hubbard chain, this involves two bosonic algebras which apply to {\it all} values of $U$, electronic density, and magnetization. Only at zero magnetization does this lead to the usual charge - spin separation. We show that our ``pseudoparticle'' operator approach clarifies, unifies, and extends several recent results, including the existence of independent right and left equations of motion and the concept of ``pseudoparticle'' (also known as ``Bethe quasiparticle'').