Spectral sum rules for the Tomonaga-Luttinger model

TL;DR

This paper derives spectral sum rules for the Tomonaga-Luttinger model, aiding the interpretation of photoemission spectra in quasi-one-dimensional conductors without relying on explicit Green's function calculations.

Contribution

It presents a generalized analytical expression for spectral functions and explores the non-commuting limits of frequency and band cutoff, extending prior work by Suzumura.

Findings

Spectral sum rules are established without explicit Green's functions.

The non-commutativity of infinite frequency and cutoff limits is demonstrated.

Numerical spectra illustrate the sum rules and their applicability.

Abstract

In connection with recent publications we discuss spectral sum rules for the Tomonaga-Luttinger model without using the explicit result for the one-electron Green's function. They are usefull in the interpretation of recent high resolution photoemission spectra of quasi-one-dimensional conductors. It is shown that the limit of infinite frequency and band cut\-off do not commute. Our result for arbitrary shape of the interaction potential generalizes an earlier discussion by Suzumura. A general analytical expression for the spectral function for wave vectors far from the Fermi wave vector $k_{F}$ is presented. Numerical spectra are shown to illustrate the sum rules.