Weak-coupling expansions for the attractive Holstein and Hubbard models

TL;DR

This paper develops weak-coupling expansions for the attractive Holstein and Hubbard models, including all bandstructure and vertex corrections, showing how quantum fluctuations affect transition temperatures and can be incorporated into existing theories.

Contribution

It introduces a comprehensive weak-coupling expansion method for these models that accounts for all relevant corrections and demonstrates how to incorporate quantum fluctuations into Migdal-Eliashberg theory.

Findings

Quantum fluctuations renormalize transition temperatures by factors of order unity.

Quantum fluctuations can be incorporated into Migdal-Eliashberg theory by renormalizing phonon frequency and interaction strength.

The approach includes all bandstructure and vertex correction effects.

Abstract

Weak-coupling expansions (conserving approximations) are carried out for the attractive Holstein and Hubbard models (on an infinite-dimensional hypercubic lattice) that include all bandstructure and vertex correction effects. Quantum fluctuations are found to renormalize transition temperatures by factors of order unity, but may be incorporated into the superconducting channel of Migdal-Eliashberg theory by renormalizing the phonon frequency and the interaction strength.