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In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order $N$ and plugged into the Dyson equation, which is then solved for the propagator $G_N$. For two simple examples of fermionic models -- the Hubbard atom at half filling and its zero space-time dimensional simplified version -- we find that $G_N$ converges when $Ntoinfty$ to a limit $G_infty,$, which coincides with the exact physical propagator $G_{rm exact} ,$ at small enough coupling, while $G_infty eq G_{rm exact} ,$ at strong coupling. We also demonstrate that it is possible to discriminate between these two regimes thanks to a criterion which does not require the knowledge of $G_{rm exact} ,$, as proposed in [Rossi et al., PRB 93, 161102(R) (2016)].
Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional Hubbard model as an example to demonstrate its capability a
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 important properties such as total energies or photoemiss
Many-body perturbation theory is often formulated in terms of an expansion in the dressed instead of the bare Greens function, and in the screened instead of the bare Coulomb interaction. However, screening can be calculated on different levels of ap
The carrier-density dependence of the photoemission spectrum of the Holstein many-polaron model is studied using cluster perturbation theory combined with an improved cluster diagonalization by Chebychev expansion.
The bandstructure of gold is calculated using many-body perturbation theory (MBPT). Different approximations within the GW approach are considered. Standard single shot G0W0 corrections shift the unoccupied bands up by ~0.2 eV and the first sp-like o