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 (plus or minus) one. The hallmark of the transition scenario is a splitting of the number density distortion into a half-integer core and a large halo carrying the complementary charge plus/minus 1/2. The sign of the halo charge changes across the transition. The radius of the halo diverges on the approach to the critical strength of the center.
ICTP Seminar Series in Condensed Matter and Statistical Physics "Trapping Centers at the Superfluid-Mott-Insulator Criticality: Transition between Charge-quantized States"