Trapping centers at the superfluid-Mott-insulator criticality: Transition between charge-quantized states

Under the conditions of superfluid-Mott-insulator criticality in two dimensions, the trapping centers-i.e., local potential wells and bumps-are generically characterized by an integer charge corresponding to the number of trapped particles (if positive) or holes (if negative). Varying the strength of the center leads to a transition between two competing ground states with charges differing by +/- 1. The hallmark of the transition scenario is a splitting of the number density distortion delta n(r) into a half-integer core and a large halo carrying a complementary charge of +/- 1/2. The sign of the halo changes across the transition and the radius of the halo r(0) diverges on the approach to the critical strength of the center, V = V-c, by the law r(0) alpha |V - V-c|-((nu) over tilde), with (nu) over tilde approximate to 2.33(5).