TY - JOUR
T1 - Physical and unphysical regimes of self-consistent many-body perturbation theory
AU - Van Houcke, Kris
AU - Kozik, Evgeny
AU - Rossi, Riccardo
AU - Deng, Youjin
AU - Werner, Felix
N1 - Publisher Copyright:
Copyright K. Van Houcke et al.
PY - 2024/5/27
Y1 - 2024/5/27
N2 - 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 GN. 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 GN converges when N → ∞ to a limit G∞ , which coincides with the exact physical propagator Gexact at small enough coupling, while G∞ ≠ Gexact at strong coupling. This follows from the findings of [1] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the G∞ = Gexact and G∞ ≠ Gexact regimes thanks to a criterion which does not require the knowledge of Gexact , as proposed in [2].
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 GN. 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 GN converges when N → ∞ to a limit G∞ , which coincides with the exact physical propagator Gexact at small enough coupling, while G∞ ≠ Gexact at strong coupling. This follows from the findings of [1] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the G∞ = Gexact and G∞ ≠ Gexact regimes thanks to a criterion which does not require the knowledge of Gexact , as proposed in [2].
UR - http://www.scopus.com/inward/record.url?scp=85196054291&partnerID=8YFLogxK
U2 - 10.21468/SciPostPhys.16.5.133
DO - 10.21468/SciPostPhys.16.5.133
M3 - Article
SN - 2542-4653
VL - 16
SP - 133
JO - SciPost Physics
JF - SciPost Physics
IS - 5
M1 - 133
ER -