On Migdal's theorem and the pseudogap

TL;DR

This paper investigates the limitations of Migdal's theorem in a model of quasiparticles coupled to spin or charge fluctuations, revealing conditions where a pseudogap forms and Migdal's theorem fails, especially near magnetic boundaries.

Contribution

It demonstrates the breakdown of Migdal's theorem in certain regimes, leading to pseudogap formation and spectral anomalies not predicted by mean-field theories.

Findings

Pseudogap opens in the quasiparticle spectrum near magnetic boundaries.

The pseudogap is strongly anisotropic, vanishing along the Brillouin zone diagonal.

Quasiparticle peak splitting occurs in ferromagnetic fluctuation regimes.

Abstract

We study a model of quasiparticles on a two-dimensional square lattice coupled to Gaussian distributed dynamical molecular fields. The model describes quasiparticles coupled to spin or charge fluctuations, and is solved by a Monte Carlo sampling of the molecular field distributions. When the molecular field correlations are sufficiently weak, the corrections to the self-consistent Eliashberg theory do not bring about qualitative changes in the quasiparticle spectrum. But for a range of model parameters near the magnetic boundary, we find that Migdal's theorem does not apply and the quasiparticle spectrum is qualitatively different from its mean-field approximation, in that a pseudogap opens in the quasiparticle spectrum. An important feature of the magnetic pseudogap found in the present calculations is that it is strongly anisotropic. It vanishes anlong the diagonal of the Brillouin zone and is large near the zone boundary. In the case of ferromagnetic fluctuations, we also find a range of model parameters with qualitative changes in the quasiparticle spectral function not captured by the one-loop approximation, in that the quasiparticle peak splits into two. We provide intuitive arguments to explain the physical origin of the breakdown of Midgal's theorem