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Effects of electron correlations on Anderson insulators have been one of thecentral themes for recent two decades, suggesting that the Anderson insulatingphase turns into a novel insulating state referred to as many body localization(MBL). However, the role of spin degrees of freedom in this dynamical phasetransition still remains unclarified as a function of the interaction strength.In this study, we perform real-space spin-resolved Hartree-Fock-Andersonsimulations to investigate metal-insulator transitions above a criticaldisorder strength in three spatial dimensions, where all single-particle statesare Anderson-localized without interactions. Here, relatively weak correlationsbelow the Mott regime are taken into account in the mean-field fashion butdisorder effects are introduced essentially exactly. We find two types ofsingle-particle mobility edges, where the multifractal spectrum of theinteraction-driven low-energy mobility edge deviates from that of thehigh-energy one smoothly connected with the multifractal spectrum of themetal-insulator transition without interactions. We show that the weaklyinteracting insulating phase remains to be a paramagnetic Anderson insulatingstate up to the temperature of the order of the band width. On the other hand,we uncover that the relatively strongly interacting insulating phase stillbelow the Mott regime is ferromagnetic, which turns into a ferromagneticmetallic state at a critical temperature much lower than the order of thebandwidth. Based on all these results, we propose a quantum phase transitionfrom a paramagnetic Anderson insulating state to a ferromagnetic MBL insulatingphase via an intermediate ferromagnetic metallic state, which intervenesbetween these two insulators at the Fermi energy.

Quantum phase transition from a paramagnetic Anderson insulating state  to a ferromagnetic many-body localized state via an intermediate  ferromagnetic metallic phase