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arXiv:cond-mat/0702571 · Journal of Physics Condensed Matter

Electron and phonon dispersions of the two-dimensional Holstein model: effects of vertex and non-local corrections

J. P. Hague

Published Apr 22, 2003• 26 citations
arXivHTMLPDF

Abstract

I apply the newly developed dynamical cluster approximation (DCA) to the calculation of the electron and phonon dispersions in the two-dimensional Holstein model. In contrast to previous work, the DCA enables the effects of spatial fluctuations (non-local corrections) to be examined. Approximations neglecting and incorporating lowest-order vertex corrections are investigated. I calculate the phonon density of states, the renormalized phonon dispersion, the electron dispersion and electron spectral functions. I demonstrate how vertex corrections stabilize the solution, stopping a catastrophic softening of the (π, π) phonon mode. A kink in the electron dispersion is found in the normal state along the (ζ, ζ) symmetry direction in both the vertex- and non-vertex-corrected theories for low phonon frequencies, corresponding directly to the renormalized phonon frequency at the (π, 0) point. This kink is accompanied by a sudden drop in the quasi-particle lifetime. Vertex and non-local corrections enhance the effects at large bare phonon frequencies.

DOI
10.1088/0953-8984/15/17/309

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We extend the dynamical vertex approximation (DΓΓΓA), in its most commonly used ladder-version, to systems with retarded electronic interactions. Such an extended scheme, which we name "dynamical-UUU DΓΓΓA", allows us to study strongly interacting electrons coupled to bosons including non-local spatial correlations on all length scales on top of the purely local ones captured by dynamical mean-field theory. We demonstrate the applicability of the method in the specific case of the coupling to a single dispersionless phononic mode, by studying the Hubbard-Holstein model on the square and cubic lattices, focusing on regimes of sizable Hubbard interactions where strong electronic correlations compete with phonon-mediated interactions. As illustrative examples, we consider the antiferromagnetic phase in the three-dimensional model and the d-wave superconductor in two dimensions, analyzing the effect of the electron-phonon coupling, including its frequency dependence, on both instabilities.
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