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We describe the effect of competing interactions and symmetry breaking 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 ω0 and interaction strengths are performed within the framework of the dynamical mean field theory combined with the
numerical renormalization group. I will discuss advantages and drawbacks of these methods.
First the ground state phase diagram of the HH model at half filling is established.
It is found to be either antiferromagnetically ordered (AFM) or charge ordered depending on U, g, and ω0. The quantum phase transition between the states is continuous for small couplings and large phonon frequencies ω0 and becomes discontinuous for large couplings
and small values of ω0. The relevance of these results for BaBiO3 is discussed [1,2].
Motivated by the observation in copper-oxide high-temperature superconductors,
we investigate the appearance of kinks in the electronic dispersion due to
coupling to phonons for a system with strong electronic repulsion.
Paramagnetic DMFT solutions in the presence of large repulsion show a kink
only for large values of the electron-phonon coupling λ or large
doping and, contrary to the conventional electron-phonon theory, the position
of such a kink can be shifted to energies larger than the renormalized phonon frequency ω0r. When including antiferromagnetic correlations we find a stronger effect of the electron-phonon interaction on the electronic
dispersion due to a cooperative effect and a visible kink at ω0r, even for smaller λ. Our results provide a scenario of a kink position increasing with doping, which can be related to recent photoemission experiments on Bi-based cuprates [3].
[1] J Bauer, EPL 90 (2010), 27002. [2] J Bauer and AC Hewson, Phys. Rev. B 81 (2010), 235113. [3] J Bauer and G Sangiovanni, cond-mat/1007.5268. |
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