  We introduce an integrable spin ladder model and study its exact solution,
correlation functions, and entanglement properties. The model supports two
particle types (corresponding to the even and odd sub-lattices), such that the
scattering phases are constants: particles of the same type scatter as free
fermions, whereas the inter-particle phase shift is a constant tuned by an
interaction parameter. Therefore, the spin ladder bears similarities with
anyonic models. We present exact results for the spectrum and correlation
functions, and we study the sub-lattice entanglement by numerical means.
