A variational approach for the Quantum Inverse Scattering Method

Abstract

We introduce a variational approach for the Quantum Inverse Scattering Method to exactly solve a class of Hamiltonians via Bethe ansatz methods. We undertake this in a manner which does not rely on any prior knowledge of integrability through the existence of a set of conserved operators. The procedure is conducted in the framework of Hamiltonians describing the crossover between the low-temperature phenomena of superconductivity, in the Bardeen-Cooper-Schrieffer (BCS) theory, and Bose-Einstein condensation (BEC). The Hamiltonians considered describe systems with interacting Cooper pairs and a bosonic degree of freedom. We obtain general exact solvability requirements which include seven subcases which have previously appeared in the literature.

18 pages, no eps figures

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• Integrability of an extended d+id-wave pairing Hamiltonian
• On the exact solvability of the anisotropic central spin model: An operator approach
• Solvable 2D superconductors with l-wave pairing