Diagrammatic perturbation theory and the pseudogap

TL;DR

This paper investigates a 2D quasiparticle model coupled to dynamical fields, comparing non-perturbative Monte Carlo solutions with diagrammatic perturbation theory, revealing limitations of the latter in capturing pseudogap phenomena near magnetic boundaries.

Contribution

It demonstrates that diagrammatic perturbation theory fails to reproduce key features of the pseudogap in certain parameter regimes, highlighting the need for non-perturbative approaches.

Findings

Diagrammatic methods capture qualitative features when correlations are weak.

Monte Carlo reveals a double peak structure in the quasiparticle spectrum near magnetic boundary.

Perturbation theory cannot reproduce the pseudogap and spin-splitting phenomena.

Abstract

We study a model of quasiparticles on a two-dimensional square lattice coupled to Gaussian distributed dynamical fields. The model describes quasiparticles coupled to spin or charge fluctuations and is solved by a Monte Carlo sampling of the molecular field distributions. The non-perturbative solution is compared to various approximations based on diagrammatic perturbation theory. When the molecular field correlations are sufficiently weak, the diagrammatic calculations capture the qualitative aspects of the quasiparticle spectrum. For a range of model parameters near the magnetic boundary, we find that the quasiparticle spectrum is qualitatively different from that of a Fermi liquid in that it shows a double peak structure, and that the diagrammatic approximations we consider fail to reproduce, even qualitatively, the results of the Monte Carlo calculations. This suggests that the pseudogap induced by a coupling to antiferromagnetic fluctuations and the spin-splitting of the quasiparticle peak induced by a coupling to ferromagnetic spin-fluctuations lie beyond diagrammatic perturbation theory.