Local moments and magnetic order in the two-dimensional Anderson-Mott transition

We study the role of electronic correlation in a disordered two-dimensional model by using a variational wave function that can interpolate between Anderson and Mott insulators. Within this approach, the Anderson-Mott transition can be described both in the paramagnetic and in the magnetic sectors. In the latter case, we find evidence for the formation of local magnetic moments that order before the Mott transition. The charge gap opening in the Mott insulator is accompanied by the vanishing of the $\lim_{q\to 0} \overline{< n_q>< n_{-q}>}$ (the bar denoting the impurity average), which is related to the compressibility fluctuations. The role of a frustrating (second-neighbor) hopping is also discussed, with a particular emphasis to the formation of metastable spin-glass states.