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We present a worm-type Monte Carlo study of several typical models in thethree-dimensional (3D) U(1) universality class, which include the classical 3DXY model in the directed flow representation and its Villain version, as wellas the 2D quantum Bose-Hubbard (BH) model with unitary filling in theimaginary-time world-line representation. From the topology of theconfigurations on a torus, we sample the superfluid stiffness $\rho_s$ and thedimensionless wrapping probability $R$. From the finite-size scaling analysesof $\rho_s$ and of $R$, we determine the critical points as $T_c ({\rm XY})=2.201\, 844 \,1(5)$ and $T_c ({\rm Villain})=0.333\, 067\, 04(7)$ and $(t/U)_c({\rm BH})=0.059 \, 729 \,1(8)$, where $T$ is the temperature for the classicalmodels, and $t$ and $U$ are respectively the hopping and on-site interactionstrength for the BH model. The precision of our estimates improvessignificantly over that of the existing results. Moreover, it is observed thatat criticality, the derivative of a wrapping probability with respect to $T$suffers from negligible leading corrections and enables a precise determinationof the correlation length critical exponent as $\nu=0.671 \, 83(18)$. Inaddition, the critical exponent $\eta$ is estimated as $\eta=0.038 \, 53(48)$by analyzing a susceptibility-like quantity. We believe that these numericalresults would provide a solid reference in the study of classical and quantumphase transitions in the 3D U(1) universality, including the recent developmentof the conformal bootstrap method.

High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class