Addition spectrum, persistent current, and spin polarization in coupled   quantum dot arrays: coherence, correlation, and disorder
  The ground state persistent current and electron addition spectrum in two-dimensional quantum dot arrays and one-dimensional quantum dot rings, pierced by an external magnetic flux, are investigated using the extended Hubbard model. The collective multidot problem is shown to map exactly into the strong field noninteracting finite-size Hofstadter butterfly problem at the spin polarization transition. The finite size Hofstadter problem is discussed, and an analytical solution for limiting values of flux is obtained. In weak fields we predict novel flux periodic oscillations in the spin component along the quantization axis with a periodicity given by $\nu h/e$ ($\nu \le 1$). The sensitivity of the calculated persistent current to interaction and disorder is shown to reflect the intricacies of various Mott-Hubbard quantum phase transitions in two- dimensional systems: the persistent current is suppressed in the antiferromagnetic Mott-insulating phase governed by intradot Coulomb interactions; the persistent current is maximized at the spin density wave - charge density wave transition driven by the nearest neighbor interdot interaction; the Mott-insulating phase persistent current is enhanced by the long-range interdot interactions to its noninteracting value; the strong suppression of the noninteracting current in the presence of random disorder is seen only at large disorder strengths; at half filling even a relatively weak intradot Coulomb interaction enhances the disordered noninteracting system persistent current; in general, the suppression of the persistent current by disorder is less significant in the presence of the long-range interdot Coulomb interaction. 
R. Kotlyar, C. A. Stafford, and S. Das Sarma