Internal space renormalization group for the Luttinger model

TL;DR

This paper applies the internal space renormalization group method to the Luttinger model, revealing that the theory remains strongly coupled at the Fermi points and is hindered by Landau poles, challenging the assumption of weak interactions.

Contribution

It introduces a systematic internal space RG approach to analyze the Luttinger model, highlighting strong coupling effects near the Fermi points and explaining differences with bosonized solutions.

Findings

The theory is strongly coupled at the Fermi points for any small bare coupling.

Removal of the cutoff is prevented by Landau poles.

Normal ordering explains the absence of strong coupling effects in bosonization.

Abstract

The absence of fermionic, asymptotical one-particle states in the Luttinger model raises the suspicion that the interactions are actually strong at the vicinity of the Fermi points. The functional internal space renormalization group method, a systematical scheme for the computation of effective coupling strengths off the Fermi points, is applied to shed some light on this issue. A simple truncation of the evolution equation shows that the theory is indeed strongly coupled at the Fermi points for arbitrarily small value of the bare coupling constant and the removal of the cutoff is blocked by Landau poles. A peculiar feature of the normal ordering scheme is pointed out to explain the absence of these effects in the bosonized solution.