Nonuniversal spectral properties of the Luttinger model

TL;DR

This paper analyzes the spectral functions of the Luttinger model for finite systems, revealing nonuniversal features at certain momenta and discussing implications for photoemission experiments on quasi-one-dimensional conductors.

Contribution

It introduces a simple interpretative method for spectral functions in the Luttinger model and derives analytical expressions for a simplified interaction model, highlighting nonuniversal spectral features.

Findings

Spectral functions show nonuniversal features away from Fermi points.

Analytical expressions enable thermodynamic limit analysis.

Spectral functions do not revert to noninteracting behavior at large momenta.

Abstract

The one electron spectral functions for the Luttinger model are discussed for large but finite systems. The methods presented allow a simple interpretation of the results. For finite range interactions interesting nonunivesal spectral features emerge for momenta which differ from the Fermi points by the order of the inverse interaction range or more. For a simplified model with interactions only within the branches of right and left moving electrons analytical expressions for the spectral function are presented which allows to perform the thermodynamic limit. As in the general spinless model and the model including spin for which we present mainly numerical results the spectral functions do not approach the noninteracting limit for large momenta. The implication of our results for recent high resolution photoemission measurements on quasi one-dimensional conductors are discussed.