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 pm 1. The hallmark of the transition scenario is a splitting of the number density distortion, δn(r), into a half-integer core and a large halo carrying the complementary charge of pm 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 propto |V-V_c|^{-tildeν}, with tildeν approx 2.33(5).