Bosonization and correlators of the one-dimensional Hubbard model

TL;DR

This paper derives the Luttinger liquid relations for the 1D Hubbard model, providing a simple method to calculate correlators and critical exponents across different interaction strengths using bosonization and Bethe Ansatz insights.

Contribution

It offers a straightforward derivation of the Luttinger liquid relations and correlators for the 1D Hubbard model, including the infinite U limit, with a transparent physical approach.

Findings

Derived the Luttinger liquid relation for finite and infinite U

Calculated correlators in the infinite U limit using bosonization

Expressed physical operators through charge and spin Bose fields

Abstract

We present simple derivation of the Luttinger liquid relation for the 1D Hubbard model both for finite $U$ and in the $U=\infty$ limit. We describe the simple solution of the Hubbard model in the infinite repulsion limit and use it to calculate the correlators of the model in this limit in a simple and a physical way using the Bosonization technique. We then calculate the asymptotics of the correlators of the model at arbitrary $U$ through the single parameter, which can be calculated from the Bethe Ansatz solution. Our derivation of the critical exponents is simple and allows one to express different physical operators of the Hubbard model through the charge and spin Bose fields in a direct and a physically transparent way.