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Physical and unphysical regimes of self-consistent many-body perturbation theory
by Kris Van Houcke, Evgeny Kozik, Riccardo Rossi, Youjin Deng, Félix Werner
Submission summary
| Authors (as registered SciPost users): | Félix Werner |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202102_00011v3 (pdf) |
| Date submitted: | 2024-04-16 08:29 |
| Submitted by: | Werner, Félix |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
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 $G_N$. 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 $N\to\infty$ to a limit $G_\infty\,$, which coincides with the exact physical propagator $G_{\rm exact}$ at small enough coupling, while $G_\infty \neq G_{\rm exact}$ at strong coupling. This follows from the findings of [Kozik, Ferrero and Georges, PRL 114, 156402 (2015)] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the $G_\infty=G_{\rm exact}$ and $G_\infty\neq G_{\rm exact}$ 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)].
Author comments upon resubmission
``I feel like one could improve the presentation by adding a few sentences at the end to connect the proof more explicitly with the written statements Eq.9 and Eq.10."
We implemented this suggestion by making two minor additions, listed below, and appearing in blue in the updated manuscript.
List of changes
1) We added the following sentence at the end of the appendix, to reiterate the connection with the criterion Eq.9:
``This concludes the derivation of the equality $G_\infty = G_{\rm exact}$ under the assumption (9)."
2) To connect with the simplified criterion Eq.10:
In the appendix, we prefer to stick to the derivation of the criterion Eq.9 and not to discuss Eq.10 (in accordance with the title of the Appendix and its description in the main text). Instead, we added, in the main text, the following sentence (right after Eq.10):
``Indeed, (9) implies (10), and a situation where (10) would hold while (9) would not hold seems unlikely to occur."