Luttinger parameters of interacting fermions in 1D at high energies

TL;DR

This paper demonstrates that in a 1D system of interacting spinless fermions, a Luttinger parameter influences observable spectral features beyond low energies, revealing a parabolic edge in the spectral function at high energies.

Contribution

It extends the concept of the Luttinger parameter to high-energy regimes using Bethe-Ansatz, beyond the traditional low-energy Tomonaga-Luttinger model.

Findings

Spectral function edge is parabolic at all momenta.

The edge's prefactor depends on the Luttinger parameter K.

Luttinger parameter influences high-energy spectral features.

Abstract

Interactions between electrons in one-dimension are fully described at low energies by only a few parameters of the Tomonaga-Luttinger model which is based on linearisation of the spectrum. We consider a model of spinless fermions with a short range interaction via the Bethe-Ansatz technique and show that a Luttinger parameter emerges in an observable beyond the low energy limit. A distinct feature of the spectral function, the edge that marks the lowest possible excitation energy for a given momentum, is parabolic for arbitrary momenta and the prefactor is a function of the Luttinger parameter, K.