Persistent currents in two dimensions: New regimes induced by the interplay between electronic correlations and disorder

Using the persistent current I induced by an Aharonov-Bohm flux in square lattices with random potentials, we study the interplay between electronic correlations and disorder upon the ground state (GS) of a few polarized electrons (spinless fermions) with Coulomb repulsion. K being the total momentum, we show that I is proportional to K in the continuum limit. We use this relation to distinguish between the continuum regimes, where the lattice GS behaves as in the continuum limit and I is independent of the interaction strength U when K is conserved, and the lattice regimes where I decays as U increases. Changing the disorder strength W and U, we obtain many regimes which we study using the map of local currents carried by three spinless fermions.