Berlin 2024 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 24: Quantum-Critical Phenomena
TT 24.13: Vortrag
Dienstag, 19. März 2024, 12:45–13:00, H 2053
Failure of the Baym-Kadanoff construction to match consistently quantum dynamics with thermodynamic critical behavior — Václav Janiš1, Vladislav Pokorný1, and •Šimon Kos2 — 1Institute of Physics, The Czech Academy of Sciences, Na Slovance 2, CZ-18200 Praha 8, Czech Republic — 2University of West Bohemia, Univerzitní 8, CZ-301 00 Plzeň, Czech Republic
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. Any description of critical behavior, hence, remains unreliable unless the fluctuations of the order parameter in the conserving vertex lead to a divergence coinciding with that of the dynamical vertex.
Keywords: Baym-Kadanoff construction; Schwinger-Dyson equation; Ward identity; two-particle irreducible vertex; thermodynamic consistency