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

TL;DR

This paper introduces a generalized p+ip pairing Hamiltonian that includes environmental interactions, breaking particle number conservation but maintaining integrability through advanced algebraic methods.

Contribution

It presents a new integrable model of the p+ip Hamiltonian with environmental interactions, solved via Boundary Quantum Inverse Scattering Method.

Findings

The model remains integrable despite particle exchange with environment.

Derived Bethe Ansatz Equations for exact energy spectrum.

Established integrability using non-diagonal reflection matrices.

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.