Failure of the Baym-Kadanoff construction to consistently match quantum dynamics with thermodynamic critical behavior

0585795 - FZÚ 2025 RIV US eng J - Journal Article
Janiš, Václav - Pokorný, Vladislav - Kos, Š.
Failure of the Baym-Kadanoff construction to consistently match quantum dynamics with thermodynamic critical behavior.
Physical Review B. Roč. 109, č. 7 (2024), č. článku 075171. ISSN 2469-9950. E-ISSN 2469-9969
R&D Projects: GA ČR(CZ) GF23-05263K
Institutional support: RVO:68378271
Keywords : correlated electrons * self-consistent approximations * quantum dynamics * thermodynamic consistency * dynamical vertex * conserving vertex * critical behavior
OECD category: Condensed matter physics (including formerly solid state physics, supercond.)
Impact factor: 3.7, year: 2022
Method of publishing: Open access

We disclose a serious deficiency of the Baym-Kadanoff construction of thermodynamically consistent conserving approximations. There are two vertices in this scheme: dynamical and conserving. The divergence of each indicates a phase instability. We show that each leads to incomplete and qualitatively different behavior at different critical points. The diagrammatically controlled dynamical vertex from the Schwinger-Dyson equation does not obey the Ward identity and cannot be continued beyond its singularity. The divergence in the conserving vertex, obeying the conservation laws, does not invoke critical behavior of the spectral function and the specific heat and does not comply with the Mermin-Wagner theorem. The description of the critical behavior of correlated electrons becomes consistent and reliable only if the fluctuations of the order parameter in the conserving vertex lead to a divergence coinciding with that of the dynamical one.
Permanent Link: https://hdl.handle.net/11104/0353471