Unphysical and physical solutions in many-body theories: from weak to strong correlation
Many-body theory is largely based on self-consistent equations that are constructed in terms
of the physical quantity of interest itself, for example the density. Therefore, the calculation of …
of the physical quantity of interest itself, for example the density. Therefore, the calculation of …
Approximations for many-body Green's functions: insights from the fundamental equations
G Lani, P Romaniello, L Reining - New Journal of Physics, 2012 - iopscience.iop.org
Several widely used methods for the calculation of band structures and photo emission
spectra, such as the GW approximation, rely on many-body perturbation theory. They can be …
spectra, such as the GW approximation, rely on many-body perturbation theory. They can be …
Solution to the many-body problem in one point
JA Berger, P Romaniello, F Tandetzky… - New Journal of …, 2014 - iopscience.iop.org
In this work we determine the one-body Greenʼs function as solution of a set of functional
integro-differential equations, which relate the one-particle Greenʼs function to its functional …
integro-differential equations, which relate the one-particle Greenʼs function to its functional …
Multiplicity of solutions to -type approximations
We show that the equations underlying the GW approximation have a large number of
solutions. This raises the question, how can we find the physical solution? We provide two …
solutions. This raises the question, how can we find the physical solution? We provide two …
Conditions where random phase approximation becomes exact in the high-density limit
It is shown that, in d-dimensional systems, the vertex corrections beyond the random phase
approximation (RPA) or GW approximation scales with the power d− β− α of the Fermi …
approximation (RPA) or GW approximation scales with the power d− β− α of the Fermi …
Padé resummation of many-body perturbation theories
Y Pavlyukh - Scientific Reports, 2017 - nature.com
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 …
series. Despite non-convergence, the asymptotic expansions are useful when truncated to a …
Functional approach to the electronic and bosonic dynamics of many-body systems perturbed with an arbitrary strong electron-boson interaction
A Marini, Y Pavlyukh - Physical Review B, 2018 - APS
We present a formal derivation of the many-body perturbation theory for a system of
electrons and bosons subject to a nonlinear electron-boson coupling. The interaction is …
electrons and bosons subject to a nonlinear electron-boson coupling. The interaction is …
An exactly solvable self-convolutive recurrence
RJ Martin, MJ Kearney - Aequationes mathematicae, 2010 - Springer
We consider a self-convolutive recurrence whose solution is the sequence of coefficients in
the asymptotic expansion of the logarithmic derivative of the confluent hypergeometric …
the asymptotic expansion of the logarithmic derivative of the confluent hypergeometric …
Many-body perturbation theory and non-perturbative approaches: screened interaction as the key ingredient
Many-body perturbation theory is often formulated in terms of an expansion in the dressed
instead of the bare Green's function, and in the screened instead of the bare Coulomb …
instead of the bare Green's function, and in the screened instead of the bare Coulomb …
On the Luttinger-Ward functional and the convergence of skeleton diagrammatic series expansion of the self-energy for Hubbard-like models
B Farid - arXiv preprint arXiv:2108.10903, 2021 - arxiv.org
We consider a number of questions regarding the Luttinger-Ward functional and the many-
body perturbation series expansion of the proper self-energy $\Sigma (\mathbf {k}; z) …
body perturbation series expansion of the proper self-energy $\Sigma (\mathbf {k}; z) …