Classical-quantum correspondence of special and extraordinary-log criticality: Villain?s bridge

There has been much recent progress on exotic surface critical behavior, yet the classical-quantum corre-spondence of special and extraordinary-log criticality remains largely unclear. Employing worm Monte Carlo simulations, we explore the surface criticality at an emergent superfluid-Mott insulator critical point in the Villain representation, which is believed to connect classical and quantum O(2) critical systems. We observe a special transition with the thermal and magnetic renormalization exponents y(t) = 0.58(1) and y(h) = 1.690(1), respectively, which are close to recent estimates from models with discrete spin variables. The existence of extraordinary-log universality is evidenced by the critical exponent (q) over cap = 0.58(2) from two-point correlation and the renormalization-group parameter alpha = 0.28(1) from superfluid stiffness, which obey the scaling relation of extraordinary-log critical theory and recover the logarithmic finite-size scaling of critical superfluid stiffness in open-edge quantum Bose-Hubbard model. Our results bridge recent observations of surface critical behavior in the classical statistical mechanical models [Parisen Toldin, Phys. Rev. Lett. 126, 135701 (2021); Hu et al., ibid. 127, 120603 (2021); Parisen Toldin et al., ibid. 128, 215701 (2022)] and the open-edge quantum Bose-Hubbard model [Sun et al., arXiv:2205.00878 (2022)].