Renormalization of the Coulomb interaction in one-dimensional electron systems

TL;DR

This paper uses renormalization group methods and GW approximation to analyze how the Coulomb interaction affects low-energy properties of one-dimensional electron systems, revealing wavefunction and velocity renormalizations while maintaining Luttinger liquid behavior.

Contribution

It introduces a detailed renormalization analysis of unscreened Coulomb interactions in 1D systems, highlighting the effects on wavefunction and Fermi velocity.

Findings

Wavefunction renormalization is significant

Fermi velocity is renormalized by interactions

System remains in the Luttinger liquid universality class

Abstract

Renormalization group methods are used to study the low-energy behavior of the unscreened Coulomb interaction in a one-dimensional electron system. By applying a GW approximation, a strong wavefunction renormalization is found in the model, as well as renormalization of the Fermi velocity. This may have significant effects depending on the filling level of the system. The effective couplings remain bounded at arbitrarily low energies so that, in spite of the long-range character of the interaction, the system still falls into the Luttinger liquid universality class.