  The spectral properties and phase diagram of the exact integrable spin one
quantum chain introduced by Alcaraz and Bariev are presented. The model has a
U(1) symmetry and its integrability is associated to an unknown R-matrix whose
dependence on the spectral parameters is not of difference form. The associated
Bethe ansatz equations, that fix the eigenspectra, are distinct from those
associated to other known integrable spin models. The model has a free
parameter $t_p$. We show that at the special point $t_p=1$ the model gets an
extra U(1) symmetry and reduces to the deformed SU(3) Perk-Schultz model at a
special value of its anisotropy $q=\exp(i2\pi/3)$ andin the presence of an
external magnetic field. Our analysis is done either by solving the associated
Bethe-ansatz equations or by direct diagonalization of thequantum Hamiltonian
for small lattice sizes. The phase diagram is calculated by exploring the
consequences of conformal invariance on the finite-size corrections of the
Hamiltonian eigenspectrum. The model exhibits a critical phase ruled by $c=1$
conformal field theory separated from a massive phase by first-order phase
transitions.
