PHASE-DIAGRAM OF THE 2-DIMENSIONAL ANDERSON-HUBBARD MODEL

We study the ground state of the two-dimensional Anderson-Hubbard mode l using a quantum real space renormalization group method. We obtain t he phase diagram near half filling. The system is always insulating wi th disorder. At half filling, the system undergoes a transition from a gapless (Anderson) insulator to an incompressible (Mott-Hubbard) insu lator as the interaction U reaches a critical value U(c). Away from ha lf filling, the insulating phase is always gapless and is found to be controlled by the Anderson fixed point at half filling. This result is similar to that obtained in the corresponding one-dimensional system and suggests strongly the importance of the electron-electron correlat ion in this gapless insulating phase.