Phonon Self-Energy Effects in Migdal-Eliashberg Theory

TL;DR

This paper reviews recent two-dimensional electron-phonon model studies, comparing Quantum Monte Carlo and Migdal-Eliashberg theory, revealing how electron filling influences charge density wave and superconductivity competition.

Contribution

It provides new insights into electron-phonon interactions and competing orders using both computational and theoretical approaches in a 2D model.

Findings

Half-filled band favors charge density wave order.

Away from half-filling, charge density wave suppresses superconductivity.

Quantum Monte Carlo and Migdal-Eliashberg results are compared.

Abstract

Recent work on an electron-phonon model in two-dimensions is reviewed and some new results are presented. We utilize both Quantum Monte Carlo simulations and Migdal-Eliashberg theory. The type of electron-ion coupling considered is on-site. Competing instabilities are charge density wave (CDW) and singlet superconductivity. When the electron band is half-filled, the charge density wave dominates. Away from half-filling CDW correlations actually suppress superconductivity.