Iterated perturbation theory for the attractive Holstein and Hubbard models

TL;DR

This paper applies truncated perturbation theory to the attractive Holstein and Hubbard models in infinite dimensions, comparing results with Monte Carlo simulations to evaluate accuracy in calculating transition temperatures and self energies.

Contribution

It demonstrates the effectiveness and limitations of second and fourth order iterated perturbation theory for these models, especially in predicting transition temperatures and self energies.

Findings

Second order iterated perturbation theory accurately predicts transition temperatures.

Self energy is well-reproduced, but vertex functions are less accurate.

Near half filling, the theory shows anomalous, non-conserving behavior.

Abstract

A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact Monte Carlo results. The second order iterated perturbation theory is shown to be quite accurate in calculating transition temperatures for retarded interactions, but is not as accurate for the self energy or the irreducible vertex functions themselves. Iterated perturbation theory is carried out thru fourth order for the Hubbard model. The self energy is quite accurately reproduced by the theory, but the vertex functions are not. Anomalous behavior occurs near half filling because the iterated perturbation theory is not a conserving approximation. (REPLACED WITH UUENCODED FIGURES AT THE END. THE TEXT IS UNCHANGED)