Running coupling constants of the Luttinger liquid

TL;DR

This paper calculates the running coupling constants in the Luttinger liquid model, revealing nontrivial scaling laws and Landau poles, and clarifies the apparent contradiction with beta function expectations.

Contribution

It provides the first detailed computation of running coupling constants in the Luttinger liquid, highlighting their scaling behavior and the presence of Landau poles.

Findings

Identification of nontrivial scaling laws

Discovery of Landau poles in the model

Resolution of the beta function contradiction

Abstract

Two running coupling constants of the Luttinger liquid are computed in the fermion-fermion and fermion-antifermion channels. Nontrivial scaling laws are found together with Landau poles. The apparent contradiction with the expected vanishing of the beta functions is explained.