Regensburg 2025 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 41: Quantum-Critical Phenomena (joint session TT/DY)

TT 41.10: Talk

Thursday, March 20, 2025, 12:00–12:15, H31

Critical behavior of the 1d superconductor in the FLEX approximation — •Šimon Kos¹, Sunil D'Souza¹, Jan Gebel¹, Ján Minár¹, and Václav Janiš² — ¹University of West Bohemia, Univerzitní 8, CZ-301 00 Plzeň, Czech Republic — ²Institute of Physics, The Czech Academy of Sciences, Na Slovance 2, CZ-18200 Praha 8, Czech Republic

The dynamical quantum fluctuations below the lower critical dimension push the superconducting critical point to zero temperature. We study the quantum critical behavior of the 1d superconductor with one-particle self-consistency provided by the FLEX approximation within the canonical Baym-Kadanoff scheme. We use the non-interacting singlet electron-electron bubble in the two-particle vertex of the Schwinger-Dyson equation, allowing for a qualitatively correct and tractable treatment of the low-energy critical behavior compatible with the Mermin-Wagner theorem. We use a polar approximation to transform the convolutive Schwinger-Dyson equation into an algebraic one that can be solved semi-analytically. We confirm the position of the critical point and assess the low-temperature behavior of the Hubbard model with attractive interaction.

Keywords: 1d superconductor; one-particle self-consistency; FLEX approximation; Schwinger-Dyson equation; Mermin-Wagner theorem