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

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)].

11 pages, 6 figures

References in corpus (42)

• Critical Exponents of the N-vector model
• Worm algorithms for classical statistical models
• The Theory of Boundary Critical Phenomena
• Quantum criticality with two length scales
• The superconductor-insulator transition in 2D dirty boson systems
• Bond and Site Percolation in Three Dimensions
• Simultaneous analysis of three-dimensional percolation models
• The dynamics of quantum criticality via Quantum Monte Carlo and holography
• Critical phenomena at perfect and non-perfect surfaces
• Topological Luttinger Liquids from Decorated Domain Walls
• Surface and bulk transitions in three-dimensional O(n) models
• Cluster Monte Carlo Algorithm for the Quantum Rotor Model
• Unconventional Surface Critical Behaviors Induced by Quantum Phase Transition from Two-Dimensional Affleck-Kennedy-Lieb-Tasaki Phase to Néel Order
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Universal Conductivity in a Two-Dimensional Superfluid-to-Insulator Quantum Critical System
• Boundary critical behavior of the three-dimensional Heisenberg universality class
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• Finite-size scaling above the upper critical dimension
• Engineering Surface Critical Behavior of (2+1)-Dimensional O(3) Quantum Critical Points
• High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class
• Shape-dependent universality in percolation
• Universal Scaling of the Conductivity at the Superfluid-Insulator Phase Transition
• Nonordinary criticality at the edges of planar spin-1 Heisenberg antiferromagnets
• On the role of Fourier modes in finite-size scaling above the upper critical dimension
• Extraordinary-log surface phase transition in the three-dimensional $XY$ model
• Nonordinary edge criticaliy of two-dimensional quantum critical magnets
• Continuous Néel-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry
• Random-length Random Walks and Finite-size scaling in high dimensions
• A Monte Carlo study of surface critical phenomena: The special point
• Magnetic impurities at quantum critical points: large-$N$ expansion and SPT connections
• Geometric explanation of anomalous finite-size scaling in high dimensions
• Surface criticality of antiferromagnetic Potts model
• Exact solution of the anisotropic special transition in the O(n) model in 2D
• Finite-size Scaling of O($n$) Systems at the Upper Critical Dimensionality
• Spin vs. bond correlations along dangling edges of quantum critical magnets
• The Two-Dimensional Disordered Boson Hubbard Model: Evidence for a Direct Mott Insulator-to-Superfluid Transition and Localization in the Bose Glass Phase
• Surface critical properties of the three-dimensional clock model
• Complete graph and Gaussian fixed point asymptotics in the five-dimensional Fortuin-Kasteleyn Ising model with periodic boundaries
• A worm algorithm for the fully-packed loop model
• Percolation of the two-dimensional XY model in the flow representation
• Worm-type Monte Carlo simulation of the Ashkin-Teller model on the triangular lattice
• History-dependent percolation in two dimensions

Cited by in corpus (7)

• Extraordinary-log Universality of Critical Phenomena in Plane Defects
• Quantum extraordinary-log universality of boundary critical behavior
• Sublattice extraordinary-log phase and new special point of the antiferromagnetic Potts model
• The ordinary surface universality class of the three-dimensional O($N$) model
• Boundary criticality for the Gross-Neveu-Yukawa models
• Boundary operator product expansion coefficients of the three-dimensional Ising universality class
• Long-Range Order in a Strictly Short-Range Quasi-2D XY Model: When Critical Fluctuations Matter