Criticality of the excess energy cost due to the unit-flux-quantum external field for the $(2+1)$D superfluid-insulator transition

Yoshihiro Nishiyama

The two-dimensional ($2$D) spin-$S=1$ $XY$ model was investigated numerically as a realization of the $(2+1)$D superfluid-Mott-insulator (SF-MI) transition. The interaction paramet…