An integrable case of the p+ip pairing Hamiltonian interacting with its environment

Abstract

We consider a generalisation of the p+ip pairing Hamiltonian with external interaction terms. These terms allow for the exchange of particles between the system and its environment. As a result the u(1) symmetry associated with conservation of particle number, present in the p+ip Hamiltonian, is broken. Nonetheless the generalised model is integrable. We establish integrability using the Boundary Quantum Inverse Scattering Method, with one of the reflection matrices chosen to be non-diagonal. We also derive the corresponding Bethe Ansatz Equations, the roots of which parametrise the exact solution for the energy spectrum.

19 pages

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• Completeness of the Bethe states for the rational, spin-1/2 Richardson--Gaudin system
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• Integrability and quench dynamics in the spin-1 central spin XX model
• Ground-state energies of the open and closed $p+ip$-pairing models from the Bethe Ansatz
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• Quantum-classical duality for Gaudin magnets with boundary
• Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary
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• Exactly Solved Models and Beyond: a special issue in honour of R J Baxter's 75th birthday