The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap

Abstract

This paper studies the critical behavior of the 3d classical $\mathrm{O}(N)$ model with a boundary. Recently, one of us established that upon treating $N$ as a continuous variable, there exists a critical value $N_c>2$ such that for $2\le N<N_c$ the model exhibits a new extraordinary-log boundary universality class, if the symmetry preserving interactions on the boundary are enhanced. $N_c$ is determined by a ratio of universal amplitudes in the normal universality class, where instead a symmetry breaking field is applied on the boundary. We study the normal universality class using the numerical conformal bootstrap. We find truncated solutions to the crossing equation that indicate $N_c\approx 5$. Additionally, we use semi-definite programming to place rigorous bounds on the boundary CFT data of interest to conclude that $N_c>3$, under a certain positivity assumption which we check in various perturbative limits.

arXiv comment27+19 pages, 12 figures

References in corpus (59)

• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Precision Islands in the Ising and $O(N)$ Models
• The Bootstrap Program for Boundary CFT_d
• Bootstrapping the O(N) Vector Models
• The Theory of Boundary Critical Phenomena
• Conformal Field Theories Near a Boundary in General Dimensions
• Carving Out the Space of 4D CFTs
• Bootstrapping Conformal Field Theories with the Extremal Functional Method
• More constraining conformal bootstrap
• Bootstrapping the O(N) Archipelago
• Carving out OPE space and precise $O(2)$ model critical exponents
• Boundary and Interface CFTs from the Conformal Bootstrap
• Gapless topological phases and symmetry-enriched quantum criticality
• Intrinsically Gapless Topological Phases
• Gapless Symmetry Protected Topological Order
• Defects in conformal field theory
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Bootstrapping Heisenberg Magnets and their Cubic Instability
• Eliminating leading corrections to scaling in the 3-dimensional O(N)-symmetric phi^4 model: N=3 and 4
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• Monte Carlo study of an improved clock model in three dimensions
• Particle-Hole Symmetry and the Composite Fermi Liquid
• Topological Luttinger Liquids from Decorated Domain Walls
• Surface and bulk transitions in three-dimensional O(n) models
• Unconventional Surface Critical Behaviors Induced by Quantum Phase Transition from Two-Dimensional Affleck-Kennedy-Lieb-Tasaki Phase to Néel Order
• Taming the $\epsilon$-expansion with Large Spin Perturbation Theory
• Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
• An Analytic Approach to BCFT${}_d$
• Synthetic Topological Qubits in Conventional Bilayer Quantum Hall Systems
• Analytic Bootstrap for Boundary CFT
• Boundary critical behavior of the three-dimensional Heisenberg universality class
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• CFT in AdS and boundary RG flows
• Monte Carlo study of a generalized icosahedral model on the simple cubic lattice
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• Engineering Surface Critical Behavior of (2+1)-Dimensional O(3) Quantum Critical Points
• Bootstrapping boundary-localized interactions
• Nonordinary criticality at the edges of planar spin-1 Heisenberg antiferromagnets
• Radial coordinates for defect CFTs
• Surface critical behaviors of coupled Haldane chains
• Leading CFT constraints on multi-critical models in d>2
• Extraordinary-log surface phase transition in the three-dimensional $XY$ model
• Nonordinary edge criticaliy of two-dimensional quantum critical magnets
• Critical O(N) model to order ${\epsilon }^4$ from analytic bootstrap
• The structure of the spectrum of anomalous dimensions in the N-vector model in 4-epsilon dimensions
• Continuous Néel-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry
• Operator expansions, layer susceptibility and two-point functions in BCFT
• Global symmetry and conformal bootstrap in the two-dimensional $O(n)$ model
• Conformal bootstrap for percolation and polymers
• On the stability problem in the O(N) nonlinear sigma model
• Conformal Bootstrap Analysis for Yang-Lee Edge Singularity
• Three-dimensional $O(N)$-invariant ${\varphi }^4$ models at criticality for $N\ge 4$
• Topology and edge states survive quantum criticality between topological insulators
• Conformal Bootstrap Analysis for Single and Branched Polymers
• Chirality-Protected Majorana Zero Modes at the Gapless Edge of Abelian Quantum Hall States
• Superconformal Boundaries in $4-\epsilon$ dimensions
• Extraordinary transition in the two-dimensional O(n) model

Cited by in corpus (47)

• Quantum criticality under decoherence or weak measurement
• The critical O(N) CFT: Methods and conformal data
• Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
• Symmetry protected topological phases under decoherence
• Spin Impurities, Wilson Lines and Semiclassics
• Bootstrapping line defects with $O(2)$ global symmetry
• New Developments in the Numerical Conformal Bootstrap
• Notes on a Surface Defect in the $O(N)$ Model
• Analytic bootstrap for the localized magnetic field
• A plane defect in the 3d O$(N)$ model
• A dispersion relation for defect CFT
• The $g$-function and Defect Changing Operators from Wavefunction Overlap on a Fuzzy Sphere
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• Surface criticality of antiferromagnetic Potts model
• The epsilon expansion of the O$(N)$ model with line defect from conformal field theory
• Conformal dispersion relations for defects and boundaries
• Solving Conformal Defects in 3D Conformal Field Theory using Fuzzy Sphere Regularization
• Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite $\mathbf{\epsilon }$
• RG flows on two-dimensional spherical defects
• Quantum phase transition between topologically distinct quantum critical points
• Comments on epsilon expansion of the O$(N)$ model with boundary
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Surface critical properties of the three-dimensional clock model
• Extraordinary-log Universality of Critical Phenomena in Plane Defects
• Special Transition and Extraordinary Phase on the Surface of a Two-Dimensional Quantum Heisenberg Antiferromagnet
• Analytic bootstrap for magnetic impurities
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• Quantum extraordinary-log universality of boundary critical behavior
• The O(N)-flavoured replica twist defect
• Classical-quantum correspondence of special and extraordinary-log criticality: Villain's bridge
• Bulk and Surface Critical Behaviors of quantum Heisenberg antiferromagnet on a two-dimensional coupled diagonal ladders
• Sublattice extraordinary-log phase and new special point of the antiferromagnetic Potts model
• Contrasting pseudo-criticality in the classical two-dimensional Heisenberg and ${\mathrm{RP}}^2$ models: zero-temperature phase transition versus finite-temperature crossover
• The ordinary surface universality class of the three-dimensional O($N$) model
• Boundary operator expansion and extraordinary phase transition in the tricritical O(N) model
• Universal finite-size scaling in the extraordinary-log boundary phase of three-dimensional $O(N)$ model
• Topological physics in quantum critical systems
• Extraordinary surface critical behavior induced by symmetry-protected topological state of a two-dimensional quantum magnet
• Boundary and defect criticality in topological insulators and superconductors
• Boundary criticality for the Gross-Neveu-Yukawa models
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Boundary operator product expansion coefficients of the three-dimensional Ising universality class
• Note on surface defects in multiscalar critical models
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations
• Finite-coupling spectrum of O(N) model in AdS
• Boundary critical behavior of the Gross-Neveu-Yukawa model