Ordering Phenomena in Transition Metal Oxides

Are the electron-phonon and the spin-fluctuation mediated pairing potentials enhanced or suppressed by vertex corrections?   

The effects of electronic correlations on the electron-phonon (el-ph) and on the electron-spin-fluctuation (el-sp) coupling are studied in a two-dimensional Hubbard model as a function of doping and temperature. The el-ph and el-sp vertices, which enter the corresponding boson mediated pairing potentials and which influence much-discussed issues such as the ``kinks'' in photoemission spectra, are extracted on the basis of a numerically exact quantum Monte-Carlo (QMC) technique and complimented with a diagrammatic analysis. Entering, in the case of the el-ph vertex, the physically relevant strong-correlation regime (U ≅ 8t), we find that the forward scattering process (i. e. for small phonon momenta q, ionic el-ph coupling) stops decreasing and begins to substantially increase as a function of U, leading to an effective el-ph coupling which is peaked in the forward direction. Whereas at weak and intermediate Coulomb interactions, screening is the dominant correlation effect suppressing the el-ph coupling, at larger U values irreducible vertex corrections become more important and give rise to this increase. These vertex corrections are shown to crucially depend on the renormalized electronic structure of the strongly correlated system. Our findings deviate from a Fermi-liquid description and, in contrast to approximate analytical (U = ∞) and slave-boson results are not connected to an incipient transition towards a charge instability or phase separation. Implications for the specific role of phonon modes, for the el-ph mediated d-wave pairing potential and ARPES selfenergy, and for the difference between transport and superconducting el-ph coupling constants are discussed. With a similar QMC approach, we have studied whether the spin-fluctuation mediated pairing is suppressed by vertex corrections, as has previously been suggested by J. R. Schrieffer in the limit of large antiferromagnetic (AF) correction length ξ. There remains the crucial question of how large must ξ be for this effect to be substantial. We find that both the vertex and thus also the el-sp pairing potential are reduced already at very short ξs (of order Cu-Cu distance), namely as soon as the relevant electronic states form ``spin-bag'' quasiparticles.