Many-Electron Effects

Massimo Capone, Claudio Castellani, M. Grilli

The Hubbard-Holstein model is a simple model including both electron-phonon interaction and electron-electron correlations. We review a body of theoretical work investigating, the effects of strong correlations on the electron-phonon interaction. We focus on the regime, relevant to high- T c superconductors, in which the electron correlations are dominant. We find that electron-phonon interaction can still have important signatures, even if many anomalies appear, and the overall effect is far from conventional. In particular in the paramagnetic phase the effects of phonons are much reduced in the low-energy properties, while the high-energy physics can still be affected by phonons. Moreover, the electron-phonon interaction can give rise to important effects, like phase separation and charge-ordering, and it assumes a predominance of forward scattering even if the bare interaction is assumed to be local (momentum independent). Antiferromagnetic correlations reduce the screening effects due to electron-electron interactions and revive the electron-phonon effects.

S. Raimes

A. A. Shashkin, A. A. Kapustin, Eduard V. Deviatov +3 more

Strong electron–electron interactions in dilute two-dimensional electron systems in silicon lead to Pauli spin susceptibility growing critically at low electron densities. This effect originates from renormalization of the effective mass rather than the g-factor. The relative mass enhancement is system and disorder independent, which suggests that it is determined by electron–electron interactions only.

R. Starke, G. A. H. Schober

This article presents a systematic theoretical enquiry concerning the conceptual foundations and the nature of phonon-mediated electron-electron interactions. Starting from the fundamental many-body Hamiltonian, we propose a simple scheme to decouple the electrons and nuclei of a crystalline solid via effective interactions. These effective interactions, which we express in terms of linear response functions, are completely symmetric under the exchange of electrons and nuclei. Correspondingly, we derive concrete formulae for both the effective electron interaction mediated by phonons and the effective core interaction mediated by electrons. In particular, we rederive from our fundamental ansatz the well-known general expressions of the effective electron-electron interaction in terms of the elastic Green function and the phonon dispersion relation. We further show that the effective core interaction coincides in the instantaneous limit with the dynamical matrix as calculated in electronic structure theory. If combined with the Kubo formalism, our general formulae lend themselves to the calculation of effective interactions from first principles. By showing the compatibility of our approach with the functional integral formalism, this work also paves the way for the derivation of ab initio initial interactions for functional renormalization group applications.