Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions

TL;DR

This paper investigates the spectral function of interacting one-dimensional fermions, revealing how spectrum nonlinearity restores Fermi liquid features while maintaining some Luttinger liquid characteristics.

Contribution

It introduces a model that accounts for spectrum nonlinearity, bridging the gap between Fermi liquid and Luttinger liquid descriptions in one dimension.

Findings

Restoration of Lorentzian peak in spectral function on particle mass-shell

Presence of power-law singularity on hole mass-shell

Differences from traditional Tomonaga-Luttinger model

Abstract

We evaluate the spectral function of interacting fermions in one dimension. Contrary to the Tomonaga-Luttinger model, our treatment accounts for the nonlinearity of the free fermion spectrum. In a striking departure from the Luttinger liquid theory, the spectrum nonlinearity restores the main feature of the Fermi liquid: a Lorentzian peak in the spectral function on the particle mass-shell. At the same time, the spectral function displays a power-law singularity on the hole mass-shell, similar to that in the Luttinger liquid.