On Migdal’s theorem and the pseudogap

We study a model of quasiparticles on a two-dimensional square lattice coupled to Gaussian distributed dynamical molecular fields. We consider two types of such fields, a vector molecular field that couples to the quasiparticle spin-density and a scalar field coupled to the quasiparticle number density. 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 Eliashberg approximation. In the range of model parameters studied, we find the transverse spin-fluctuation modes play a key role. While a pseudogap opens when quasiparticles are coupled to antiferromagnetic fluctuations, such a pseudogap is not observed in the corresponding charge-fluctuation case for the range of parameters studied, where vertex corrections are found to effectively reduce the strength of the interaction. This suggests that one has to be closer to the border of long-range order to observe pseudogap effects in the charge-fluctuation