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