Impact of Retardation in the Holstein-Hubbard Model: a two-site Calculation

TL;DR

This paper investigates how electron-electron repulsion affects superconducting pairing in the Hubbard-Holstein model using exact diagonalization on a two-site system, revealing a stronger negative impact than previously thought.

Contribution

It provides a rigorous analysis of retardation effects and Coulomb interactions in a two-site Hubbard-Holstein model, highlighting the more detrimental influence of direct electron-electron repulsion.

Findings

Electron-electron repulsion significantly hampers pairing.

Retardation effects are less effective in mitigating Coulomb repulsion.

Exact diagonalization offers precise insights into two-site interactions.

Abstract

Eliashberg theory provides a theoretical framework for understanding the phenomenon of superconductivity when pairing between two electrons is mediated by phonons, and retardation effects are fully accounted for. However, when a direct Coulomb interaction between two electrons is also present, this interaction is only partially accounted for. In this work we use a well-defined Hamiltonian, the Hubbard-Holstein model, to examine this competition more rigorously, using exact diagonalization on a two-site system. We find that the direct electron-electron repulsion between two electrons has a significantly more harmful effect on pairing than suggested through the standard treatment of this interaction.