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

The main objective of this project is to develop methods for the exactand efficient calculation of correlation functions of local operators inintegrable lattice models. In previous work we have shown that thecorrelation functions of the spin-1/2 Heisenberg chain and of relatedintegrable models are characterized by a specific structure, similar toWick's theorem for free Fermions, which we have called a `hiddenFermionic structure': longer-range correlation functions arepolynomials in one-point functions and neighbour-correlators, whosecoefficients are determined by the representation theory of theunderlying infinite-dimensional symmetry algebra. Here we plan toutilize our experience with the derivation of universal functionalequations in order to study the question if similar hidden algebraicstructures exist for the higher-spin realizations of the integrableHeisenberg chains or for integrable lattice models connected withaffine quantum groups of higher rank.

• DFG Programme: Research Grants
• Co-Investigators: Professor Dr. Frank Göhmann; Professor Dr. Andreas Kluemper