Riassunto analitico
Many-body perturbation theory (MBPT) is a theoretical framework
large used to study ground and excited state properties of materials and molecules.
Within Green's function (GF) theory, this approach leads to an effective one-particle problem,
involving a dynamical self-energy, that is self-consistent in the one-particle GF.
Working diagrammatically, a number of different approximations of the self-energy operator are
available, including GW, 2B, or SOSEX (the latter being less investigated than the former ones).
In this work we mainly deal with the second-order screened exchange (SOSEX)
correlation self energy, in comparison with the HF, GW, and 2B approximations.
To do so, we take advantage of the in-house AGWX code, implementing many-body methods on a lattice,
where we implement all the required extensions to deal with the SOSEX self-energy.
Specifically, we exploit a sum over pole (SOP) representation of propagators,
including Green's functions, polarizabilities, and self-energies.
This approach is numerically very stable and allows for an accurate treatment of dynamical operators,
in turn enabling the possibility to perform self-consistent Green's function simulations.
First, we check the validity of our implementation, by using analytical
results from the Hubbard dimer as a function of U/t.
Then we consider Hubbard chains of finite length in order to assess and discuss the features
and quality of the SOSEX self-energy, in different flavours,
by numerically comparing with other approximations (such as GW and 2B), and with
the exact results obtained by full CI.
The limits of applicability of the SOSEX self-energies are discussed.
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