QUANTUM
   INTEGRABLE
   SYSTEMS and
   GEOMETRY
   2012









 3-7 SEPTEMBER 2012
 OLHÃO, PORTUGAL

Algebraic Bethe Ansatz for deformed Gaudin model

Nuno Cirlio António

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The Gaudin model based on the sl(2)-invariant r-matrix with an extra Jordanian term depending on the spectral parameters is considered. The appropriate creation operators defining the Bethe states of the system are constructed through a recurrence relation. The commutation relations between the generating function t(\lambda) of the integrals of motion and the creation operators are calculated and therefore the algebraic Bethe Ansatz is fully implemented. The energy spectrum as well as the corresponding Bethe equations of the system coincide with the ones of the sl(2)-invariant Gaudin model. As opposed to the sl(2)-invariant case, the operator t(\lambda) and the Gaudin Hamiltonians are not Hermitian.