Competition between Electron-Phonon Attraction and Weak Coulomb Repulsion

The Holstein-Hubbard model is examined in the limit of infinite dimensions. Conventional wisdom states that charge-density-wave (CDW) order is more strongly affected by Coulomb repulsion than superconducting order (SC) because of the pseudopotential effect. We find that the CDW-SC phase boundary does move toward half filling as the Coulomb repulsion increases, but, surprisingly, the CDW transition temperature is initially more robust against Coulomb repulsion than the superconducting transition temperature. This puzzling feature is resolved by an analysis of weak-coupling perturbation theory.