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

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.

29 pages

References in corpus (4)

• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• Off-diagonal Bethe ansatz solution of the XXX spin-chain with arbitrary boundary conditions
• Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
• Quasi-classical descendants of disordered vertex models with boundaries

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• Ground-state Bethe root densities and quantum phase transitions
• A Q-operator for open spin chains I: Baxter's TQ relation
• Integrability, multifractality, and two-photon dynamics in disordered Tavis-Cummings models
• Quantum-classical duality for Gaudin magnets with boundary
• Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary
• "Bethe-Ansatz-free" eigenstates of spin-1/2 Richardson-Gaudin integrable models
• Freidel-Maillet type presentations of $U_q(s{l}_2)$