  The Haldane-Shastry model is one of the most studied interacting spin
systems. The Yangian symmetry makes it exactly solvable, and the model has
semionic excitations. We introduce disorder into the Haldane-Shastry model by
allowing the spins to sit at random positions on the unit circle and study the
properties of the eigenstates. At weak disorder, the spectrum is similar to the
spectrum of the clean Haldane-Shastry model. At strong disorder, the long-range
interactions in the model do not decay as a simple power law. The eigenstates
in the middle of the spectrum follow a volume law, but the coefficient is
small, and the entropy is hence much less than for an ergodic system. In
addition, the energy level spacing statistics is neither Poissonian nor of the
Wigner-Dyson type. The behavior at strong disorder hence serves as an example
of a non-ergodic phase, which is not of the many-body localized kind, in a
model with long-range interactions and SU(2) symmetry.
