Parquet approach - the <i>most fundamental </i>diagrammatic method?

In this talk we show that the parquet equation follows as natural and in fact completely analogous to well known diagrammatic equations like the Dyson or the Bethe-Salpeter equation. Furthermore, it has been shown that other well known methods like the GW approximation or the functional Renormalization Group (fRG) method emerge as ways to find an approximate solution to the parquet equation [1][2].
This makes the parquet approach a very fundamental one and raises interest in approximate solutions to the parquet equation.
We here present an approximate way to solve the parquet equation using the method of Truncated Unities[3]. We apply it to the 2D Hubbard model reaching temperatures and system sizes that were previously hardly accessible by unbiased methods. We find deviations from mean field behaviour like the pseudogap-phase.

[1] F. Krien, A. Kauch, K. Held, 2020 arXiv:2009.12868
[2] F. Kugler J. Delft, 2019 New J. Phys. 21 099601
[3] C. Eckhardt, C. Honerkamp, K. Held, A. Kauch, 2020 Phys. Rev. B 101, 155104