Impact of Retardation in the Holstein-Hubbard Model

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 an adaptive modification of the Trugman method on an infinite lattice. 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.