Work

Physical and unphysical regimes of self-consistent many-body perturbation theory

Year: 2024

Type: article

Abstract: 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 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 G N converges when N\to∞ N → ∞ to a limit G_∞\, G ∞ , which coincides with the exact physical propagator G_{exact} G e x a c t at small enough coupling, while G_∞ ≠ G_{exact} G ∞ ≠ G e x a c t 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} G ∞ = G e x a c t and G_∞≠G_{exact} G ∞ ≠ G e x a c t regimes thanks to a criterion which does not require the knowledge of G_{exact} G e x a c t , as proposed in [Phys. Rev. B 93, 161102 (2016)].

Source: SciPost Physics

DOI: 10.21468/scipostphys.16.5.133

Authors: Kris Van Houcke, Evgeny Kozik, Riccardo Rossi, Youjin Deng, Félix Werner