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

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 $λ$ due to electron-phonon coupling approximately coincide, $U\simeq λ$. We find a continuous transition for small coupling and large $ω_0$, and a discontinuous one for large coupling and/or small $ω_0$. 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.