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Journal of Physics A Mathematical and Theoretical

Non-skew-symmetric classicalr-matrices and integrable cases of the reduced BCS model

T. Skrypnyk

Published Nov 6, 2009• 46 citations
Publisher

Abstract

We consider generalized quantum Gaudin systems in an external magnetic field associated with non-skew-symmetric sl (2)-valued classical r -matrices. We calculate spectra of the generating function of the corresponding Hamiltonians using the algebraic Bethe ansatz. We apply these results to the construction of integrable fermionic Hamiltonians of a generalized BCS type. We investigate the special cases when the corresponding integrable Hamiltonians contain only a pairing interaction term and consider an example of such a situation associated with a special non-skew-symmetric r -matrix.

DOI
10.1088/1751-8113/42/47/472004

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We construct generalized Gaudin systems in an external magnetic field corresponding to arbitrary so(3)-valued non-skew-symmetric r-matrices with spectral parameters and non-homogeneous external magnetic fields. In the case of r-matrices diagonal in the sl(2) basis we calculate the spectrum and the eigen-values of the corresponding generalized Gaudin hamiltonians using the algebraic Bethe ansatz. We explicitly consider several one-parametric families of non-skew-symmetric classical r-matrices and the corresponding generalized Gaudin systems in a magnetic field. We apply these results to fermionic systems and obtain a wide class of new integrable fermionic BCS-type hamiltonians.
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