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Integrability of Hubbard model and Algebraic Geometry

Theoretisch-Physikalisches Seminar, 26.01.2018


Over the years the one-dimensional Hubbard model has been an exception among the majority of model solvable by Bethe ansatz methods. We shall discuss the integrability of the Hubbard model towards the view of the theory of Algebraic Geometry. We shall argue that the weights of the classical statistical system whose transfer matrix commutes with the Hubbard Hamiltonian sit on an elliptic curve. By way of contrast the respective R-matrix lie on an Abelian surface being birational to the product of two distinct elliptic curves. This clarifies the reason why the R-matrix cannot be expressed using only the difference of spectral parameters. Interesting enough the Lax operator keeps the unitarity and crossing properties of standard factorizable relativistic scattering theories.


Prof. Dr. Marcio Martins, Universidade Federal de Sao Carlos, Brasilien


Institut für Theoretische Physik

Date 26.01.2018
16:15 o'clock - 18:00 o'clock
Location Physikgebäude, Building: 3701
Room: 268
Großer Seminarraum
Appelstraße 2
30167 Hannover