  Using the well-known trigonometric six-vertex solution of the Yang-Baxter
equation we derive an integrable pairing Hamiltonian with anyonic degrees of
freedom. The exact algebraic Bethe ansatz solution is obtained using standard
techniques. From this model we obtain several limiting models, including the
pairing Hamiltonian with p+ip-wave symmetry. An in-depth study of the p+ip
model is then undertaken, including a mean-field analysis, analytic and
numerical solution of the Bethe ansatz equations, and an investigation of the
topological properties of the ground-state wavefunction. Our main result is
that the ground-state phase diagram of the p+ip model consists of three phases.
There is the known boundary line with gapless excitations that occurs for
vanishing chemical potential, separating the topologically trivial strong
pairing phase and the topologically non-trivial weak pairing phase. We argue
that a second boundary line exists separating the weak pairing phase from a
topologically trivial weak coupling BCS phase, which includes the Fermi sea in
the limit of zero coupling. The ground state on this second boundary line is
the Moore-Read state.
