The BCS model and the off shell Bethe ansatz for vertex models

Luigi Amico A, G. Falci, Rosario Fazio

Published Jan 1, 2000• 21 citations

Abstract

Abstract. We study the connection between the BCS pairing model and the inhomogeneous vertex model. The two spectral problems coincide in the quasi– classical limit of the off–shell Bethe Ansatz of the disordered six vertex model. The latter problem is transformed into an auxiliary spectral problem which corresponds to the diagonalization of the integrals of motion of the BCS model. A generating functional whose quasi classical expansion leads to the constants of motion of the BCS model and in particular the Hamiltonian, is identified. PACS: 03.65.Fd, 74.20.Fg

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The BCS model and the off shell Bethe ansatz for vertex models

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Published Jan 1, 2000• 21 citations

OpenAlex

Abstract

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\mathbf{K}

-matrix construction and taking the quasiclassical limit, one obtains a complete set of conserved quantities

{\mathbf{H}}_{i}

from which the DBCS Hamiltonian can be constructed as a second order polynomial. The eigenvalues and eigenstates of the

{\mathbf{H}}_{i}

(which reduce to the Gaudin Hamiltonians in the limit of infinitely strong coupling) are exactly known in terms of a set of parameters determined by a set of on-shell Bethe ansatz equations, which reproduce Richardson's equations for these parameters. We thus clarify that the integrability of the DBCS model is a special case of the integrability of the twisted inhomogeneous XXX vertex model. Furthermore, by considering the twisted inhomogeneous XXZ model and/or choosing a generic polynomial of the

{\mathbf{H}}_{i}

's as Hamiltonian, more general exactly solvable models can be constructed. To make the paper accessible to readers that are not Bethe-ansatz experts, the introductory sections include a self-contained review of those of its feature which are needed here.