Universal Luttinger Liquid Relations in the 1D Hubbard Model

TL;DR

This paper demonstrates that the 1D extended Hubbard model exhibits universal Luttinger liquid behavior, with critical exponents and response functions following universal relations, confirmed through non-perturbative methods.

Contribution

It provides a rigorous, non-perturbative proof of Luttinger liquid relations in the 1D Hubbard model using Renormalization Group and Ward Identities.

Findings

Response functions decay with anomalous power-laws and logarithmic corrections.

Critical exponents and physical quantities satisfy universal Luttinger liquid relations.

Established Borel summability and weak spin-charge separation in the model.

Abstract

We study the 1D extended Hubbard model with a weak repulsive short-range interaction in the non-half-filled band case, using non-perturbative Renormalization Group methods and Ward Identities. At the critical temperature, T = 0, the response functions have anomalous power-law decay with multiplicative logarithmic corrections. The critical exponents, the susceptibility and the Drude weight verify the universal Luttinger liquid relations. Borel summability and (a weak form of) Spin-Charge separation is established.