Completeness of the Bethe states for the rational, spin-1/2 Richardson--Gaudin system

Abstract

Establishing the completeness of a Bethe Ansatz solution for an exactly solved model is a perennial challenge, which is typically approached on a case by case basis. For the rational, spin-1/2 Richardson--Gaudin system it will be argued that, for generic values of the system's coupling parameters, the Bethe states are complete. This method does not depend on knowledge of the distribution of Bethe roots, such as a string hypothesis, and is generalisable to a wider class of systems.

15 pages. Submission to SciPost. Minor corrections made in this version in response to referee reports

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Cited by in corpus (14)

• Integrability and dark states in an anisotropic central spin model
• Exact quantum dynamics of XXZ central spin problems
• Solution of the classical Yang--Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunneling model
• Inner products in integrable Richardson-Gaudin models
• Integrable spin-1/2 Richardson-Gaudin XYZ models in an arbitrary magnetic field
• Quadratic operator relations and Bethe equations for spin-1/2 Richardson-Gaudin models
• The spin-s homogeneous central spin model: exact spectrum and dynamics
• Common framework and quadratic Bethe equations for rational Gaudin magnets in arbitrarily oriented magnetic fields
• Integrability and quench dynamics in the spin-1 central spin XX model
• A variational method for integrability-breaking Richardson-Gaudin models
• Ground-state energy of a Richardson-Gaudin integrable BCS model
• On the exact solvability of the anisotropic central spin model: An operator approach
• Dark states in an integrable XY central spin model
• "Bethe-Ansatz-free" eigenstates of spin-1/2 Richardson-Gaudin integrable models