Competing interactions and symmetry breaking in the Hubbard-Holstein model

Johannes Bauer

Max Planck Instiuite

We analyze the effect of competing interactions in strongly correlated  electron  systems. We focus on the competition of the instantaneous  short range Coulomb interaction $U$ with the retarded electron-electron  interaction induced by an electron-phonon coupling $g$ as described by the  Hubbard-Holstein (HH) model. Controlled calculations for arbitrary phonon  frequencies $\omega_0$ and interaction strengths are performed  within the framework of the dynamical mean field theory combined with the  numerical renormalization group.   First the ground state phase diagram of the HH model at half filling is  established.  It is found to be either antiferromagnetically ordered or charge  ordered  depending on $U$, $g$, and $\omega_0$.  The  quantum phase transition between the states is continuous for small  couplings and large  phonon frequencies $\omega_0$ and becomes discontinuous for large couplings  and small values of $\omega_0$.  We present results for the static  and dynamic electronic and bosonic properties near the transition.   We discuss further studies in this setup away from half filling.  There superconductivity and retardation effects can be analyzed and compared  with earlier approaches such as the one by Morel and Anderson.  Also the effect of the coupling to the phonons on the electronic dispersion  and specifically the appearance of kinks, and how they are modified in the  presence of $U$, is discussed.