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arXiv · 1601.04285

Taming singularities of the diagrammatic many-body perturbation theory

Yaroslav Pavlyukh·Jamal Berakdar·Angel Rubio
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Abstract

In a typical scenario the diagrammatic many-body perturbation theory generates asymptotic series. Despite non-convergence, the asymptotic expansions are useful when truncated to a finite number of terms. This is the reason for popularity of leading-order methods such as $GW$ approximation in condensed matter, molecular and atomic physics. Emerging higher-order implementations suffer from the appearance of nonsimple poles in the frequency-dependent Green's functions and negative spectral densities making self-consistent determination of the electronic structure impossible. Here a method based on the Pad\'e approximation for overcomming these difficulties is proposed and applied to the Hamiltonian describing a core electron coupled to a single plasmonic excitation. By solving the model purely diagrammatically, expressing the self-energy in terms of combinatorics of chord diagrams, and regularizing the diverging perturbative expansions using the Pad\'e approximation the spectral function is determined self-consistently using 3111 diagrams up to the sixth order.

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Yaroslav Pavlyukh, Jamal Berakdar, Angel Rubio. 2016-01-17. Taming singularities of the diagrammatic many-body perturbation theory. https://arxiv.org/abs/1601.04285

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