Universal functional equations for spectrum, thermodynamics and correlation functions of integrable lattice models

• Applicant: Professor Dr. Hermann Boos
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields ; Mathematics
• Term: from 2018 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 398579888

• Final Report Year: 2023

Final Report Abstract

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.

Publications

• 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.