Trapping Centers at the Superfluid-Mott-insulator Criticality: Transition between Charge-quantized States

Abstract

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, $\hat{I}´n(r)$, 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 $r_0\propto |V-V_c{|}^{-\tilde{\hat{I}}½}$, with $\tilde{\hat{I}}½\approx 2.33(5)$.

5 pages, 5 figures