Conserving approximations for the attractive Holstein and Hubbard models

TL;DR

This paper investigates conserving approximations in the attractive Holstein and Hubbard models, highlighting their qualitative accuracy in predicting transition temperature behavior despite quantitative limitations.

Contribution

It demonstrates that finite-order conserving approximations better capture quantitative details than infinite summations, while still maintaining correct qualitative trends.

Findings

Finite-order conserving approximations are more accurate than infinite summations.

Infinite summation approximations correctly predict a peak in transition temperature.

All effects of nonconstant density of states and vertex corrections are included.

Abstract

Conserving approximations are applied to the attractive Holstein and Hubbard models (on an infinite-dimensional hypercubic lattice). All effects of nonconstant density of states and vertex corrections are taken into account in the weak-coupling regime. Infinite summation of certain classes of diagrams turns out to be a quantitatively less accurate approximation than truncation of the conserving approximations to a finite order, but the infinite summation approximations do show the correct qualitative behavior of generating a peak in the transition temperature as the interaction strength increases.