Localized magnetic field in the $O(N)$ model

Abstract

We consider the critical $O(N)$ model in the presence of an external magnetic field localized in space. This setup can potentially be realized in quantum simulators and in some liquid mixtures. The external field can be understood as a relevant perturbation of the trivial line defect, and thus triggers a defect Renormalization Group (RG) flow. In agreement with the $g$-theorem, the external localized field leads at long distances to a stable nontrivial defect CFT (DCFT) with $g<1$. We obtain several predictions for the corresponding DCFT data in the epsilon expansion and in the large $N$ limit. The analysis of the large $N$ limit involves a new saddle point and, remarkably, the study of fluctuations around it is enabled by recent progress in AdS loop diagrams. Our results are compatible with results from Monte Carlo simulations and we make several predictions that can be tested in the future.

arXiv comment50 pages, 11 figures, 3 tables v2 minor typos fixed, references updated, matches journal

References in corpus (61)

• Critical Phenomena and Renormalization-Group Theory
• Towards a derivation of holographic entanglement entropy
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Bounding scalar operator dimensions in 4D CFT
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Writing CFT correlation functions as AdS scattering amplitudes
• Quantum Field Theory in the Large N Limit: a review
• Quantum magnetism and criticality
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• The Bootstrap Program for Boundary CFT_d
• Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality
• Boundary conformal field theory approach to the two-dimensional critical Ising model with a defect line
• Conformal Field Theories Near a Boundary in General Dimensions
• Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics
• On the Boundary Entropy of One-dimensional Quantum Systems at Low Temperature
• Effective Conformal Theory and the Flat-Space Limit of AdS
• Bootstrapping the 3d Ising twist defect
• Overscreened multi-channel SU(N) Kondo model : large-N solution and Conformal Field Theory
• Analyticity and the Holographic S-Matrix
• Multicritical phenomena in O(n_1)+O(n_2)-symmetric theories
• Quantum Impurity in a Nearly Critical Two Dimensional Antiferromagnet
• Boundary and Interface CFTs from the Conformal Bootstrap
• Defects in conformal field theory
• The g-theorem and quantum information theory
• Quantum impurity dynamics in two-dimensional antiferromagnets and superconductors
• Anomalies, Conformal Manifolds, and Spheres
• A Study of Quantum Field Theories in AdS at Finite Coupling
• Renyi Entropies for Free Field Theories
• Towards a $C$-theorem in defect CFT
• Renormalization Group Flows on Line Defects
• Eikonal Methods in AdS/CFT: BFKL Pomeron at Weak Coupling
• Defect Lines in the Ising Model and Boundary States on Orbifolds
• Eikonal Methods in AdS/CFT: Regge Theory and Multi-Reggeon Exchange
• Line and surface defects for the free scalar field
• Spinning AdS Loop Diagrams: Two Point Functions
• Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
• CFT in AdS and boundary RG flows
• Quantum impurity in an antiferromagnet: non-linear sigma model theory
• Loops in AdS: From the Spectral Representation to Position Space
• Spectral function of a localized fermion coupled to the Wilson-Fisher conformal field theory
• The Kondo effect in bosonic spin liquids
• Monodromy Defects from Hyperbolic Space
• A Scaling Limit for Line and Surface Defects
• Monodromy Defects in Free Field Theories
• Critical behavior in the presence of an order-parameter pinning field
• Static hole in a critical antiferromagnet: field-theoretic renormalization group
• Free energy and defect $C$-theorem in free scalar theory
• Critical adsorption near edges
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• Monopole operators from the $4-\epsilon$ expansion
• Magnetic impurities at quantum critical points: large-$N$ expansion and SPT connections
• Two Point Functions in Defect CFTs
• Lower bound on the entropy of boundaries and junctions in 1+1d quantum critical systems
• Critical phenomena at edges and corners
• Moduli Anomalies and Local Terms in the Operator Product Expansion
• Conformal Bootstrap near the edge
• Osborn Equation and Irrelevant Operators
• Fusion of conformal defects in four dimensions
• Magnetic defect line in a critical Ising bath
• Boundary Conformal Field Theory at Large Charge
• Boundary quantum criticality in models of magnetic impurities coupled to bosonic baths

Cited by in corpus (35)

• The critical O(N) CFT: Methods and conformal data
• Spin Impurities, Wilson Lines and Semiclassics
• Bootstrapping line defects with $O(2)$ global symmetry
• Broken global symmetries and defect conformal manifolds
• Notes on a Surface Defect in the $O(N)$ Model
• A Scaling Limit for Line and Surface Defects
• Analytic bootstrap for the localized magnetic field
• A dispersion relation for defect CFT
• The $g$-function and Defect Changing Operators from Wavefunction Overlap on a Fuzzy Sphere
• Phases of Wilson Lines in Conformal Field Theories
• Line Defect RG Flows in the $\epsilon$ Expansion
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• The epsilon expansion of the O$(N)$ model with line defect from conformal field theory
• Defects in scalar field theories, RG flows and Dimensional Disentangling
• Solving Conformal Defects in 3D Conformal Field Theory using Fuzzy Sphere Regularization
• RG flows on two-dimensional spherical defects
• Comments on epsilon expansion of the O$(N)$ model with boundary
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Renormalization group flows in AdS and the bootstrap program
• RG Flows and Stability in Defect Field Theories
• Analytic bootstrap for magnetic impurities
• Polyakov blocks for the 1D CFT mixed correlator bootstrap
• Defects, Rigid Holography and $C$-theorems
• Conformal line defects at finite temperature
• Defect Localized Entropy: Renormalization Group and Holography
• Wilson loops in Large Symmetric Representations through a Double-Scaling Limit
• Critical crossover phenomena driven by symmetry-breaking defects at quantum transitions
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Probing Defects with Quantum Simulator Snapshots
• A Fuzzy Sphere Journey in Critical Phenomena
• The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere
• Fine Spectrum from Crude Analytic Bootstrap
• Casimir effect in critical $\mathrm{O}(N)$ models from non-equilibrium Monte Carlo simulations
• Finite-coupling spectrum of O(N) model in AdS