  A spin-1 atomic gas in an optical lattice, in the unit-filling Mott Insulator
(MI) phase and in the presence of disordered spin-dependent interaction, is
considered. In this regime, at zero temperature, the system is well described
by a disordered rotationally-invariant spin-1 bilinear-biquadratic model. We
study, via the density matrix renormalization group algorithm, a bounded
disorder model such that the spin interactions can be locally either
ferromagnetic or antiferromagnetic. Random interactions induce the appearance
of a disordered ferromagnetic phase characterized by a non-vanishing value of
spin-glass order parameter across the boundary between a ferromagnetic phase
and a dimer phase exhibiting random singlet order. The study of the
distribution of the block entanglement entropy reveals that in this region
there is no random singlet order.
