Competition between antiferromagnetic and charge order in the Hubbard-Holstein model

TL;DR

This paper investigates the competition between antiferromagnetic and charge order in the Hubbard-Holstein model at half filling, revealing how the transition depends on electron-electron and electron-phonon interactions, with results on phase behavior and spectral properties.

Contribution

It provides a detailed analysis of the phase diagram and transition nature in the Hubbard-Holstein model using dynamical mean field theory and numerical renormalization group methods, highlighting the conditions for continuous and discontinuous transitions.

Findings

Transition occurs when $U \,\approx\, \lambda$

Continuous transition for small coupling and large phonon frequency

Discontinuous transition for large coupling or small phonon frequency

Abstract

We study the competition between an instantaneous local Coulomb repulsion and a boson mediated retarded attraction, as described by the Hubbard-Holstein model. Restricting to the case of half filling, the ground-state phase diagram and the transitions from antiferromagnetically ordered states to charge ordered states are analyzed. The calculations are based on the model in large dimensions, so that dynamical mean field theory can be applied, and the associated impurity problem is solved using the numerical renormalization group method. The transition is found to occur when electron-electron coupling strength $U$ and the induced interaction $\lambda$ due to electron-phonon coupling approximately coincide, $U\simeq \lambda$. We find a continuous transition for small coupling and large $\omega_0$, and a discontinuous one for large coupling and/or small $\omega_0$. We present results for the order parameters, the static expectation values for the electrons and phonons, and the corresponding spectral functions. They illustrate the different types of behavior to be seen near the transitions. Additionally, the quasiparticle properties are calculated in the normal state, which leads to a consistent interpretation of the low energy excitations.