Diagrammatic perturbation theory and the pseudogap
Philippe H. Monthoux
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. The nonperturbative 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 nonperturbative results of the Monte Carlo calculations. This suggests that the magnetic pseudogap induced by a coupling to antiferromagnetic spin fluctuations and the spin splitting of the quasiparticle peak induced by a coupling to ferromagnetic spin fluctuations lie beyond diagrammatic perturbation theory. 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 case than for a spin-fluctuation-induced interaction under otherwise similar conditions. The diagrammatic approximations that contain first-order vertex corrections show the enhancement of the spin-fluctuation-induced interaction and the suppression of the effective interaction in the charge-fluctuation case. However, for the range of model parameters considered here, the multiple spin or charge-fluctuation exchange processes not included in the diagrammatic approximations considered are found to be important, especially for quasiparticles coupled to charge fluctuations.
arXiv:cond-mat/0309552•Physical Review B•Oct 12, 2004•4 citations