  We introduce an SU(M)-symmetric disordered bipartite spin model with unusual
characteristics. Although superficially similar to the Sachdev-Ye model, it has
several markedly different properties for M>2. In particular, it has a large
non-trivial nullspace whose dimension grows exponentially with system size. The
states in this nullspace are frustration-free, and are ground states when the
interactions are ferromagnetic. The exponential growth of the nullspace leads
to Hilbert-space fragmentation and a violation of the eigenstate thermalization
hypothesis. We demonstrate that the commutant algebra responsible for this
fragmentation is a non-trivial subalgebra of the Read-Saleur commutant algebra
of certain nearest-neighbour models such as the spin-1 biquadratic spin chain.
We also discuss the low-energy behaviour of correlations for the disordered
version of this model in the limit of a large number of spins and large M,
using techniques similar to those applied to the SY model. We conclude by
generalizing the Shiraishi-Mori embedding formalism to non-local models, and
apply it to turn some of our nullspace states into quantum many-body scars.
