Padé resummation of many-body perturbation theories

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 the popularity of leading-order methods such as the GW approximation in condensed matter, molecular and atomic physics. Appropriate truncation order required for the accurate description of strongly correlated materials is, however, not known a priori. Here an efficient method based on the Padé approximation is introduced for the regularization of perturbative series allowing to perform higher-order self-consistent calculations and to make quantitative predictions on the convergence of many-body perturbation theories. The theory is extended towards excited states where the Wick theorem is not directly applicable. Focusing on the plasmon-assisted photoemission from graphene, we treat diagrammatically electrons coupled to the excited state plasmons and predict new spectral features that can be observed in the time-resolved measurements.

Fast summation of divergent series and resurgent transseries from Meijer- G approximants

“…In some cases the perturbation expansion, or its Borel-transformed counterpart, may have its convergence limited by a pole. Physical examples of such behavior include perturbative spectral functions in Green's function theory [68] and the beta function of supersymmetric Yang-Mills theories [69]. In such cases Padé or Borel-Padé approximants are likely a better summation method than hypergeometric or Borel-hypergeometric summation.…”

Diagonal Padé approximant of the one-body Green's function: A study on Hubbard rings

“…Padé approximants have proved to be an effective tool to get estimates of unknown functions in many fields of physics an mathematics 2,12 . Their use in the calculation of electronic properties has been only partially explored, and in particular in the calculation of Green's functions it has been limited so far as ancillary tool, like for the extrapolation of the analytic continuation of the Matsubara Green's functions, or to model systems (see, for instance, [13][14][15] and references therein. )…”

“…one can readily apply formula (15) to calculate the finite version of (16) in frequency domain. We notice that the writing (16) suggests that such an approximation can be cast in terms of two Dyson equations.…”

“…Assuming that the basis set is already sufficiently large, the cost of the second and forth points remains unaltered for the greatest part (the only difference being an undramatic extension of of (15) or (14)). The main difference is calculating higher orders of the expansion of the self-energy, which requires more diagrams that those contained in expressions (20) and (21).…”

Charge-vibration interaction effects in normal-superconductor quantum dots

“…In its simple formulation, one assumes a linear coupling between the electron occupation on the dot and the oscillation's amplitude of one or more harmonic modes representing the local vibrations. This model has been theoretically investigated widely in literature with different variations, extensions, in different regimes and with various theoretical approaches , in particular using diagrammatic techniques [113][114][115][116][117][118][119][120], a resummation approach [121,122], and numerical and nonperturbative methods [123][124][125][126][127].…”