Coulomb and electron-phonon interactions in metals

TL;DR

This paper develops a diagrammatic Monte Carlo method to accurately model phonons in metals by treating Coulomb and electron-phonon interactions on equal footing, avoiding uncontrolled approximations.

Contribution

It introduces a non-perturbative, approximation-free approach for two-component Coulomb systems, enabling precise calculations of phonon spectra in metals.

Findings

Successfully computed phonon spectra and sound velocities.

Validated results against GW-approximation in different regimes.

Demonstrated feasibility of the Monte Carlo approach for complex systems.

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.