Universelle Funktionalgleichungen für Spektrum, Thermodynamik und Korrelationsfunktionen integrabler Gittermodelle

• Antragsteller: Professor Dr. Hermann Boos
• Fachliche Zuordnung: Kern- und Elementarteilchenphysik, Quantenmechanik, Relativitätstheorie, Felder ; Mathematik
• Förderung: Förderung von 2018 bis 2021
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 398579888

• Erstellungsjahr: 2023

Zusammenfassung der Projektergebnisse

The main objective of our proposal was to understand whether the structure of the correlation functions of local operators, called ‘factorization’ or ‘hidden fermionic structure’ and found in case of the spin-1/2 Heisenberg model (or the six-vertex model) related to the quantum group Uq (sl2 ), can also be established for other integrable lattice models, in particular, to those related to higher-rank quantum groups. Within the project we are reporting here we were able to obtain a factorization of the operators of length three for the isotropic sl3 invariant model in its fundamental representation. We also obtained reduced quantum Knizhnik-Zamolodchikov equations for the integrable models connected with the higher-rank quantum loop algebras.

Projektbezogene Publikationen (Auswahl)

• On the calculation of the correlation functions of the $ \newcommand{\slt}{\mathfrak{sl}_2} \newcommand{\sltr}{\mathfrak{sl}_3} \sltr$ -model by means of the reduced qKZ equation. Journal of Physics A: Mathematical and Theoretical, 51(44), 445202.
  Boos, H.; Hutsalyuk, A. & Nirov, Kh. S.
  
• Reduced qKZ equation: general case. Journal of Physics A: Mathematical and Theoretical, 53(1), 015202.
  Klümper, Andreas; Nirov, Khazret S. & Razumov, Alexander V.
  
• Vertex Models and Spin Chains in Formulas and Pictures. Symmetry, Integrability and Geometry: Methods and Applications (2019, 9, 13).
  Nirov, Khazret S. & Razumov, Alexander V.