The Gaudin model based on the sl2-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(λ) 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 sl2-invariant Gaudin model. As opposed to the sl2-invariant case, the operator t(λ) and the Gaudin Hamiltonians are not Hermitian. Finally, the inner products and norms of the Bethe states are studied.
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October 2011
Research Article|
October 05 2011
Algebraic Bethe ansatz for deformed Gaudin model
N. Cirilo António;
N. Cirilo António
a)
1Centro de Análise Funcional e Aplicações, Departamento de Matemática,
Instituto Superior Técnico
, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
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N. Manojlović;
N. Manojlović
b)
2
Grupo de Física Matemática da Universidade de Lisboa
, Av. Prof. Gama Pinto 2, PT-1649-003 Lisboa, Portugal
3Departamento de Matemática, F. C. T.,
Universidade do Algarve
, Campus de Gambelas, PT-8005-139 Faro, Portugal
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a)
Electronic mail: nantonio@math.ist.utl.pt.
b)
Electronic mail: nmanoj@ualg.pt.
c)
Electronic mail: astolin@chalmers.se.
J. Math. Phys. 52, 103501 (2011)
Article history
Received:
March 24 2010
Accepted:
September 06 2011
Citation
N. Cirilo António, N. Manojlović, A. Stolin; Algebraic Bethe ansatz for deformed Gaudin model. J. Math. Phys. 1 October 2011; 52 (10): 103501. https://doi.org/10.1063/1.3644345
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