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arXiv · 1405.7451

On the boundaries of quantum integrability for the spin-1/2 Richardson-Gaudin system

Inna Lukyanenko·Phillip Isaac·Jon Links
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Abstract

We discuss a generalised version of Sklyanin's Boundary Quantum Inverse Scattering Method applied to the spin-1/2, trigonometric sl(2) case, for which both the twisted-periodic and boundary constructions are obtained as limiting cases. We then investigate the quasi-classical limit of this approach leading to a set of mutually commuting conserved operators which we refer to as the trigonometric, spin-1/2 Richardson-Gaudin system. We prove that the rational limit of the set of conserved operators for the trigonometric system is equivalent, through a change of variables, rescaling, and a basis transformation, to the original set of trigonometric conserved operators. Moreover we prove that the twisted-periodic and boundary constructions are equivalent in the trigonometric case, but not in the rational limit.

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Inna Lukyanenko, Phillip Isaac, Jon Links. 2014-05-29. On the boundaries of quantum integrability for the spin-1/2 Richardson-Gaudin system. https://doi.org/10.1016/j.nuclphysb.2014.06.018

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