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Electron-phonon vertex in the two-dimensional one-band Hubbard model

Z. B. Huang·W. Hanke·E. Arrigoni·D. J. Scalapino
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Abstract

Using quantum Monte Carlo techniques, we study the effects of electronic correlations on the effective electron-phonon (el-ph) coupling in a two-dimensional one-band Hubbard model. We consider a momentum-independent bare ionic el-ph coupling. In the weak- and intermediate-correlation regimes, we find that the on-site Coulomb interaction $U$ acts to effectively suppress the ionic el-ph coupling at all electron- and phonon- momenta. In this regime, our numerical simulations are in good agreement with the results of perturbation theory to order $U^2$. However, entering the strong-correlation regime, we find that the forward scattering process 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 depend crucially on the renormalized electronic structure of the strongly correlated system.

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Z. B. Huang, W. Hanke, E. Arrigoni, D. J. Scalapino. 2004-01-08. Electron-phonon vertex in the two-dimensional one-band Hubbard model. https://doi.org/10.1103/physrevb.68.220507

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