Rigorous proof of Luttinger liquid behavior in the 1d Hubbard model

TL;DR

This paper provides the first rigorous proof that the one-dimensional Hubbard model exhibits Luttinger liquid behavior under certain conditions, using non-perturbative methods without relying on exact solutions.

Contribution

It introduces a non-perturbative, rigorous proof of Luttinger liquid behavior in the 1D Hubbard model, applicable beyond integrable cases.

Findings

Proof of Luttinger liquid behavior for small repulsive interactions

Applicable to densities away from half filling

Method can be extended to include additional interactions

Abstract

We give the first rigorous (non perturbative) proof of Luttinger liquid behavior in the one dimensional Hubbard model, for small repulsive interaction and values of the density different from half filling. The analysis is based on the combination of multiscale analysis with Ward identities bases on a hidden and approximate local chiral gauge invariance. No use is done of exact solutions or special integrability properties of the Hubbard model, and the results can be in fact easily generalized to include non local interactions, magnetic fields or interaction with external potentials