A Holographic Two-Impurity Kondo Model

Abstract

We propose a model of a strongly-interacting two-impurity Kondo system based on the AdS/CFT correspondence, also known as holography. In a Landau Fermi Liquid, the single-impurity Kondo effect is the screening of an impurity spin at low temperature $T$. The two-impurity Kondo model then describes the competition between the Kondo interaction and the Heisenberg interaction between two impurity spins, also called the RKKY interaction. For spin-$1/2$ impurities, that competition leads to a quantum phase transition from a Kondo-screened phase to a phase in which the two impurity spins screen one another. Our holographic model is based on a $(1+1)$-dimensional CFT description of the two-impurity Kondo model, reliable for two impurities with negligible separation in space. We consider only impurity spins in a totally anti-symmetric representation of an $SU(N)$ spin symmetry. We employ a large-$N$ limit, in which both Kondo and RKKY couplings are double-trace, and both Kondo and inter-impurity screening appear as condensation of single-trace operators at the impurities' location. We perform the holographic renormalization of our model, which allows us to identify the Kondo and RKKY couplings as boundary conditions on fields in AdS. We numerically compute the phase diagram of our model in the plane of RKKY coupling versus $T$, finding evidence for a quantum phase transition from a trivial phase, with neither Kondo nor inter-impurity screening, to a non-trivial phase, with both Kondo and anti-ferromagnetic inter-impurity screening. More generally we show, just using $SU(N)$ representation theory, that ferromagnetic correlations must be absent at leading order in the large-$N$ limit. Our holographic model may be useful for studying many open problems involving strongly-interacting quantum impurities, including for example the Kondo lattice, relevant for describing the heavy fermion compounds.

arXiv comment55 pages + one appendix, 9 figure files in pdf format

References in corpus (50)

• Kondo Physics in a Single Electron Transistor
• Wilson loops in large N field theories
• The Holographic Weyl anomaly
• A Tunable Kondo Effect in Quantum Dots
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• AdS/CFT Correspondence and Symmetry Breaking
• Quantum Criticality in Heavy Fermion Metals
• Holographic Entanglement Entropy: An Overview
• Holographic Renormalization
• On the Holographic Renormalization Group
• Heavy Fermions and Quantum Phase Transitions
• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Fractionalized Fermi liquids
• Holographic metals and the fractionalized Fermi liquid
• How to go with an RG Flow
• Zero Temperature Limit of Holographic Superconductors
• Conformal Field Theory Approach to the 2-Impurity Kondo Problem: Comparison with Numerical Renormalization Group Results
• Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT
• Boundary Conditions and Dualities: Vector Fields in AdS/CFT
• Overscreened multi-channel SU(N) Kondo model : large-N solution and Conformal Field Theory
• Quantum Criticality and Global Phase Diagram of Magnetic Heavy Fermions
• Holographic Renormalization and Ward Identities with the Hamilton-Jacobi Method
• Holographic Duals of Long Open Strings
• Supplementary material to Heavy electrons and the symplectic symmetry of spin
• Heavy electrons and the symplectic symmetry of spin
• Stable Wrapped Branes
• Holographic Lattices, Dimers, and Glasses
• Transition from overscreening to underscreening in the multichannel Kondo model: exact solution at large N
• Towards a holographic marginal Fermi liquid
• Lifshitz holography: The whole shebang
• One-loop Effective Action of the Holographic Antisymmetric Wilson Loop
• Solution of the Multichannel Coqblin-Schrieffer Impurity Model and Application to Multi-Level systems
• Integrble Models in Condensed Matter Physics
• A Holographic Model of the Kondo Effect
• SU(N) Irreducible Schwinger Bosons
• Bending branes for DCFT in two dimensions
• Holographic renormalization for irrelevant operators and multi-trace counterterms
• Solution of the two-impurity Kondo model: critical point, Fermi-liquid phase, and crossover
• A maximally supersymmetric Kondo model
• Adventures in Holographic Dimer Models
• Irrelevant deformations and the holographic Callan-Symanzik equation
• Heavy Fermions and the Kondo Lattice: a 21st Century Perspective
• Solution of the two impurity, two channel Kondo Model
• Holographic Kondo Model in Various Dimensions
• The Polyakov Loop of Anti-symmetric Representations as a Quantum Impurity Model
• High Temperature Superconductivity in the Cuprates
• Multiscale Entanglement Renormalization Ansatz for Kondo Problem
• Intermediate coupling fixed point study in the overscreened regime of generalized multichannel SU(N) Kondo models
• Exotic Kondo Effects in Metals: Magnetic Ions in a Crystalline Electric Field and Tunneling Centers
• Schwinger Bosons Approaches to Quantum Antiferromagnetism