Emergence of U(1) symmetry in the 3D XY model with Zq anisotropy

Abstract

We study the three-dimensional XY model with a Z_q anisotropic term. At temperatures T < Tc this dangerously irrelevant perturbation is relevant only above a length scale Lambda, which diverges as a power of the correlation length; Lambda ~ xi^a_q. Below Lambda the order parameter is U(1) symmetric. We derive the full scaling function controlling the emergence of U(1) symmetry and use Monte Carlo results to extract the exponent a_q for q=4,...,8. We find that a_q = a_4 (q/4)^2, with a_4 only marginally larger than 1. We discuss these results in the context of U(1) symmetry at "deconfined" quantum critical points separating antiferromagnetic and valence-bond-solid states in quantum spin systems.

4 pages, 4 figures. v2: co-author added, exact scaling function derived

References in corpus (3)

• "Deconfined" quantum critical points
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Ground States of the SU(N) Heisenberg Model

Cited by in corpus (63)

• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Imaging the Néel vector switching in the monolayer antiferromagnet MnPSe${}_3$ with strain-controlled Ising order
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Monte Carlo study of an improved clock model in three dimensions
• Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality
• Unraveling the Mott-Peierls intrigue in Vanadium dioxide
• Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical SrCu${}_2$(BO${}_3$)${}_2$
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• Emergence and spontaneous breaking of approximate O(4) symmetry at a weakly first-order deconfined phase transition
• Critical exponents can be different on the two sides of a transition: A generic mechanism
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• The (2+1)-d U(1) Quantum Link Model Masquerading as Deconfined Criticality
• Interfaces, Strings, and a Soft Mode in the Square Lattice Quantum Dimer Model
• The Renormalization Group Studies on Four Fermion Interaction Instabilities on Algebraic Spin Liquids
• Unconventional Quantum Critical Points
• Nature of finite-temperature transition in anisotropic pyrochlore Er2Ti2O7
• Cluster-glass phase in pyrochlore XY antiferromagnets with quenched disorder
• Monte Carlo Renormalization Flows in the Space of Relevant and Irrelevant Operators: Application to Three-Dimensional Clock Models
• Order-by-disorder near criticality in $XY$ pyrochlore magnets
• Order-by-disorder and magnetic field response in Heisenberg-Kitaev model on a hyperhoneycomb lattice
• Magnetism in S=1/2 Double-Perovskites with Strong Spin-Orbit Interactions
• Fermion-induced quantum critical points in two-dimensional Dirac semimetals
• From trivial to topological paramagnets: The case of ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_2^3$ symmetries in two dimensions
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Generic First-Order vs. Continuous Quantum Nucleation of Supersolidity
• Confinement transition in the QED${}_3$-Gross-Neveu-XY universality class
• Evidence of columnar order in the fully frustrated transverse field Ising model on the square lattice
• Magnetization plateaus of an easy-axis Kagomé antiferromagnet with extended interactions
• Correlations and order parameter at a Coulomb-crystal phase transition in a three-dimensional dimer model
• Unconventional U(1) to ${\mathbf{Z}}_{\mathbf{q}}$ cross-over in quantum and classical $\mathbf{q}$-state clock models
• A Scaling Relation for Dangerously Irrelevant Symmetry-Breaking Fields
• Thermal valence-bond-solid transition of quantum spins in two dimensions
• Spin freezing in the disordered pyrochlore magnet NaCaCo${}_2$F${}_7$: NMR studies and Monte-Carlo simulations
• Nature of Possible Magnetic Phases in Frustrated Hyperkagome Iridate
• Renormalization group analysis of phase transitions in the two dimensional Majorana-Hubbard model
• Quantum Phase Transition between Z2 spin liquid and columnar Valence Bond Crystals on a Triangular lattice
• XY* transition and extraordinary boundary criticality from fractional exciton condensation in quantum Hall bilayer
• Unveiling the nature of three dimensional orbital ordering transitions: the case of $e_g$ and $t_{2g}$ models on the cubic lattice
• Surface critical properties of the three-dimensional clock model
• Valley-polarized nematic order in twisted moiré systems: In-plane orbital magnetism and non-Fermi liquid to Fermi liquid crossover
• Emergent O(n) Symmetry in a series of three-dimensional Potts Models
• Quantum Phase Transitions beyond the Landau's Paradigm in Sp(4) Spin System
• Compass and Kitaev models -- Theory and Physical Motivations
• Buckling transitions and clock order of two-dimensional Coulomb crystals
• Emergent XY* transition driven by symmetry fractionalization and anyon condensation
• Phonon-induced rotation of the electronic nematic director in superconducting Bi${}_2$Se${}_3$
• Tunable deconfined quantum criticality and interplay of different valence-bond solid phases
• Dual dynamic scaling in deconfined quantum criticality
• Theory of quantum kagome ice and vison zero modes
• Z4-U(1) crossover of the order parameter symmetry in a two-dimensional valence-bond-solid
• Criticality of compact and noncompact quantum dissipative $Z_4$ models in $(1+1)$ dimensions
• Monte Carlo study of the critical properties of the three-dimensional 120-degree model
• Phase transitions in $q$-state clock model
• Emergent Halperin-Saslow mode and Gauge Glass in quantum Ising magnet TmMgGaO${}_4$
• Partial magnetic order in kagome spin ice
• New renormalization group study of the 3-state Potts model and related statistical models
• Phases and Phase Transitions of the Disordered Quantum Clock Model
• Relaxation Critical Dynamics with Emergent Symmetry
• Analytic framework for self-dual criticality in ${\mathbb{Z}}_k$ gauge theory with matter
• Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array
• Finite-time scaling with two characteristic time scales: Driven critical dynamics with emergent symmetry
• Intertwined order of generalized global symmetries