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

We present a worm-type Monte Carlo study of several typical models in the three-dimensional (3D) U(1) universality class, which include the classical 3D XY model in the directed flow representation and its Villain version, as well as the 2D quantum Bose-Hubbard (BH) model with unitary filling in the imaginary-time world-line representation. From the topology of the configurations on a torus, we sample the superfluid stiffness ρₛ and the dimensionless wrapping probability R. From the finite-size scaling analyses of ρₛ and of R, we determine the critical points as Tc(XY)=2.2010.16em0ex8440.16em0ex1(5) and Tc(Villain)=0.3330.16em0ex0670.16em0ex04(7) and (t/U)c(BH)=0.0590.16em0ex7290.16em0ex1(8), where T is the temperature for the classical models, and t and U are, respectively, the hopping and on-site interaction strength for the BH model. The precision of our estimates improves significantly over that of the existing results. Moreover, it is observed that at criticality, the derivative of a wrapping probability with respect to T suffers from negligible leading corrections and enables a precise determination of the correlation length critical exponent as ν=0.6710.16em0ex83(18). In addition, the critical exponent η is estimated as η=0.0380.16em0ex53(48) by analyzing a susceptibilitylike quantity. We believe that these numerical results would provide a solid reference in the study of classical and quantum phase transitions in the 3D U(1) universality, including the recent development of the conformal bootstrap method.