TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.5.133
TI  - Physical and unphysical regimes of self-consistent many-body perturbation theory
PY  - 2024/05/27
UR  - https://scipost.org/SciPostPhys.16.5.133
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 5
SP  - 133
A1  - Van Houcke, Kris
AU  - Kozik, Evgeny
AU  - Rossi, Riccardo
AU  - Deng, Youjin
AU  - Werner, Félix
AB  - 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 $G_N$. We consider two examples of fermionic models, the Hubbard atom at half filling and its zero space-time dimensional simplified version. First, we show that $G_N$ converges when $N\to∞$ to a limit $G_∞\,$, which coincides with the exact physical propagator $G_{exact}$ at small enough coupling, while $G_∞ ≠ G_{exact}$ at strong coupling. This follows from the findings of [Phys. Rev. Lett. 114, 156402 (2015)] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the $G_∞=G_{exact}$ and $G_∞≠G_{exact}$ regimes thanks to a criterion which does not require the knowledge of $G_{exact}$, as proposed in [Phys. Rev. B 93, 161102 (2016)].
ER  -

@Article{10.21468/SciPostPhys.16.5.133,
	title={{Physical and unphysical regimes of self-consistent many-body perturbation theory}},
	author={Kris Van Houcke and Evgeny Kozik and Riccardo Rossi and Youjin Deng and Félix Werner},
	journal={SciPost Phys.},
	volume={16},
	pages={133},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.5.133},
	url={https://scipost.org/10.21468/SciPostPhys.16.5.133},
}