Disordered spinor Bose-Hubbard model

We study the zero temperature phase diagram of the disordered spin-1 Bose-Hubbard model in a 2-dimensional square lattice. To this aim, we use a mean field Gutzwiller ansatz and a probabilistic mean field perturbation theory. The spin interaction induces two different regimes corresponding to a ferromagnetic and antiferromagnetic order. In the ferromagnetic case, the introduction of disorder reproduces analogous features of the disordered scalar Bose-Hubbard model, consisting in the formation of a Bose glass phase between Mott insulator lobes. In the antiferromagnetic regime the phase diagram differs more from the scalar case. Disorder in the chemical potential can lead to the disappearance of Mott insulator lobes with odd integer filling factor and, for sufficiently strong spin coupling, to Bose glass of singlets between even filling Mott insulator lobes. Disorder in the spinor coupling parameter results in the appearance of a Bose glass phase only between the n and n+1 lobes for n odd. Disorder in the scalar Hubbard interaction inhibits Mott insulator regions for occupation larger than a critical value.