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

TL;DR

This study investigates the classical-quantum correspondence of special and extraordinary-log criticality at a superfluid-Mott insulator transition using Monte Carlo simulations, revealing universal critical exponents and scaling relations.

Contribution

It provides the first detailed numerical evidence connecting classical surface critical behavior with quantum models, clarifying the universality of extraordinary-log criticality.

Findings

Observed critical exponents close to recent models with discrete spins

Confirmed the scaling relation of extraordinary-log critical theory

Revealed logarithmic finite-size scaling in superfluid stiffness

Abstract

There has been much recent progress on exotic surface critical behavior, yet the classical-quantum correspondence 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 $\hat{q}=0.58(2)$ 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 $et$ $al.$, Phys. Rev. B 106, 224502 (2022)].