Coulomb and electron-phonon interactions in metals

Abstract

An accurate and consistent theory of phonons in metals requires that all long-range Coulomb interactions between charged particles (electrons and ions) be treated on equal footing. So far, all attempts to deal with this non-perturbative system were relying on uncontrolled approximations in the absence of small parameters. In this work, we develop the Diagrammatic Monte Carlo approach for a two-component Coulomb system that obtains the solution to this fundamental problem in an approximation free way by computing vertex corrections from higher-order skeleton graphs. The feasibility of the method is demonstrated by calculating the spectrum of longitudinal acoustic phonons in a simple cubic lattice, determining their sound velocity, and obtaining the phonon spectral densities by analytic continuation of the Matsubara Green's functions. Final results are checked against the lowest-order fully self-consistent GW-approximation in both adiabatic and non-adiabatic regimes.

5 pages, 5 figures

References in corpus (4)

• Diagrammatic Monte Carlo method for many-polaron problems
• Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins
• Bold Diagrammatic Monte Carlo technique for frustrated spin systems
• Retardation effects and the Coulomb pseudopotential in the theory of superconductivity

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