Spectral Function of 2D Fermi Liquids

TL;DR

This paper demonstrates that the spectral function of 2D Fermi liquids exhibits Lorentzian behavior at low energies, confirming the stability of Landau quasiparticles, and highlights limitations of perturbative methods.

Contribution

It clarifies the spectral function shape in 2D Fermi liquids and discusses the inaccuracies of common approximation techniques.

Findings

Spectral function is Lorentzian at low energies.

Landau quasiparticles have well-defined spectral weight and small decay rates.

Perturbation theory shows deviations from Fermi liquid behavior.

Abstract

We show that the spectral function for single-particle excitations in a two-dimensional Fermi liquid has Lorentzian shape in the low energy limit. Landau quasi-particles have a uniquely defined spectral weight and a decay rate which is much smaller than the quasi-particle energy. By contrast, perturbation theory and the T-matrix approximation yield spurious deviations from Fermi liquid behavior, which are particularly pronounced for a linearized dispersion relation.