Dynamic response functions for the Holstein-Hubbard model

TL;DR

This paper investigates the dynamical correlation functions of the Holstein-Hubbard model at zero temperature, revealing how electron-electron and electron-phonon interactions influence metal-insulator transitions using advanced numerical methods.

Contribution

It provides new insights into the interplay of Coulomb repulsion and phonon effects in the Holstein-Hubbard model through detailed dynamical mean field theory calculations.

Findings

Coulomb repulsion dominates in the metallic regime.

Charge fluctuations are suppressed, decoupling electrons from phonons.

Phonon propagator softens near the bipolaronic transition, not near the Mott transition.

Abstract

We present results on the dynamical correlation functions of the particle-hole symmetric Holstein-Hubbard model at zero temperature, calculated using the dynamical mean field theory which is solved by the numerical renormalization group method. We clarify the competing influences of the electron-electron and electron-phonon interactions particularity at the different metal to insulator transitions. The Coulomb repulsion is found to dominate the behaviour in large parts of the metallic regime. By suppressing charge fluctuations, it effectively decouples electrons from phonons. The phonon propagator shows a characteristic softening near the metal to bipolaronic transition but there is very little softening on the approach to the Mott transition.