Hypergeometric resummation of self-consistent sunset diagrams for electron-boson quantum many-body systems out of equilibrium

TL;DR

This paper introduces a hypergeometric resummation method to improve convergence and preserve conservation laws in self-consistent nonequilibrium many-body perturbation calculations, demonstrated on electron-phonon systems.

Contribution

It applies hypergeometric resummation to self-consistent sunset diagrams, enhancing convergence and maintaining conservation laws in nonequilibrium quantum many-body systems.

Findings

Hypergeometric resummation accelerates convergence of self-consistent series.

The method accurately describes the convergence-limiting singularity.

Conservation laws are preserved using the resummation technique.

Abstract

A newly developed hypergeometric resummation technique [H. Mera et al., Phys. Rev. Lett. 115, 143001 (2015)] provides an easy-to-use recipe to obtain conserving approximations within the self-consistent nonequilibrium many-body perturbation theory. We demonstrate the usefulness of this technique by calculating the phonon-limited electronic current in a model of a single-molecule junction within the self-consistent Born approximation for the electron-phonon interacting system, where the perturbation expansion for the nonequilibrium Green function in powers of the free bosonic propagator typically consists of a series of non-crossing \sunset" diagrams. Hypergeometric resummation preserves conservation laws and it is shown to provide substantial convergence acceleration relative to more standard approaches to self-consistency. This result strongly suggests that the convergence of the self-consistent \sunset" series is limited by a branch-cut singularity, which is accurately described by Gauss hypergeometric functions. Our results showcase an alternative approach to conservation laws and self-consistency where expectation values obtained from conserving perturbation expansions are \summed" to their self-consistent value by analytic continuation functions able to mimic the convergence-limiting singularity structure.