Long-range interactions in a one-dimensional electron system

TL;DR

This paper investigates the effects of unscreened Coulomb interactions in a one-dimensional electron system, revealing that despite long-range interactions, the system remains within the Luttinger liquid universality class, with notable renormalizations.

Contribution

It applies renormalization group and GW methods to analyze long-range interactions, showing their impact on wavefunction and Fermi velocity renormalization in 1D electron systems.

Findings

Strong wavefunction renormalization observed

Fermi velocity is renormalized depending on filling

System remains in Luttinger liquid universality class

Abstract

We study the unscreened Coulomb interaction in a one-dimensional electron system at low-energy. We use renormalization group methods and a GW approximation, in order to analyze the model. This yields both a strong wavefunction renormalization and a renormalization of the Fermi velocity. The significance of the effects depends on the filling level of the Fermi system. Despite the long-range character of the interaction, the system still falls into the Luttinger liquid universality class, since the effective couplings remain bounded at arbitrarily low energies.