Séminaire - 25/05/2023 - Rolf SCHUMANN - From Hubbard to Heisenberg model - an analytic cluster approach

Invitation : Roland Hayn (Département PHANO, Equipe MQT).

Diffusion : IM2NP, CINaM, Irphe, LP3 (via N. Sannier), Madirel (via P. Boulet), PIIM (via T. Angot), CPT (T. Martin), Fédération de Chimie (via S. Viel), CP2M

SEMINAIRE Jeudi 25 mai 2023 à 10h30

Salle des séminaires de l'Im2np, campus de Saint-Jérôme, 1er étage Bâtiment Poincaré

Rolf SCHUMANN

University of Technology Dresden, Germany

From Hubbard to Heisenberg model - an analytic cluster approach

The lecture answers the question "Can the purely magnetic domain of the Hubbard model for arbitrarily strong on-site correlation U be described by a magnetic Heisenberg model ?" Starting from the analytical and semi-analytical solutions for the (extended) Hubbard model as well as for the spin 1/2 Heisenberg model with inclusion of cyclic terms for simple magnetic clusters, it is shown under which conditions the parameters of the Heisenberg model can be calculated from the parameters of the associated Hubbard model. As examples, the dependence of the exchange or cyclic (four-spin) interaction on the ratio U/t of the Hubbard model is given for the square and the tetrahedron. Finally, problems are discussed that arise due to the rapidly growing number of model parameters with the cluster size.