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

TL;DR

This paper investigates the behavior of trapping centers at the superfluid-Mott-insulator transition in two dimensions, revealing a charge transition characterized by a split density distortion and a diverging halo radius near criticality.

Contribution

It introduces a detailed description of the charge transition at trapping centers, including the splitting of density distortion and the critical divergence of the halo radius.

Findings

Charge quantization at trapping centers is characterized by integer charges.

Transition involves a split density distortion into a half-integer core and a large halo.

Halo radius diverges as the system approaches the critical potential strength.

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, $\delta n(r)$, 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 $r_0 \propto |V-V_c|^{-\tilde{\nu}}$, with $\tilde{\nu} \approx 2.33(5)$.