Unveiling the Kondo cloud: unitary RG study of the Kondo model

Abstract

We analyze the single-channel Kondo model using the recently developed unitary renormalization group (URG) method, and obtain a comprehensive understanding of the Kondo screening cloud. The fixed-point low-energy Hamiltonian enables the computation of a plethora of thermodynamic quantities (specific heat, susceptibility, Wilson ratio, etc.) as well as spectral functions, all of which are found to be in excellent agreement with known results. By integrating out the impurity, we obtain an effective Hamiltonian for the excitations of the electrons comprising the Kondo cloud. This is found to contain both k-space number-diagonal (Fermi liquid) as well off-diagonal four-fermion scattering terms. Our conclusions are reinforced by a URG study of the two-particle entanglement and many-body correlations among members of the Kondo cloud and impurity. The entanglement between the impurity and a cloud electron, as well as between any two cloud electrons, is found to increase under flow towards the singlet ground state at the strong-coupling fixed point. Both the number-diagonal and off-diagonal correlations within the conduction cloud are also found to increase as the impurity is screened under the flow, and the latter are found to be responsible for the macroscopic entanglement of the Kondo-singlet ground state. The unitary RG flow enables an analytic computation of the phase shifts suffered by the conduction electrons at the strong-coupling fixed point. This reveals an orthogonality catastrophe between the local moment and strong-coupling ground states, and is related to a change in the Luttinger volume of the conduction bath. Our results offer fresh insight on the nature of the emergent many-particle entanglement within the Kondo cloud, and pave the way for further investigations in more exotic contexts such as the fixed point of the over-screened multi-channel Kondo problem.

arXiv comment17 pages, 17 figures, 101 references

References in corpus (58)

• A computable measure of entanglement
• Kondo Physics in a Single Electron Transistor
• A Tunable Kondo Effect in Quantum Dots
• The numerical renormalization group method for quantum impurity systems
• Kondo physics in carbon nanotubes
• On the quantum, classical and total amount of correlations in a quantum state
• Kondo effect in a magnetic field and the magnetoresistivity of Kondo alloys
• Kondo effect in quantum dots
• Theory of Quantum Corrals and Quantum Mirages
• Universality of the Kondo Effect in a Quantum Dot out of Equilibrium
• Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
• Detecting the Kondo screening cloud around a quantum dot
• Temperature and magnetic field dependence of a Kondo system in the weak coupling regime
• The Physics of Kondo Impurities in Graphene
• Heavy-fermion and spin-liquid behavior in a Kondo lattice with magnetic frustration
• Long-range Kondo signature of a single magnetic impurity
• Spectral Properties of the Anderson Impurity Model, Comparison of Numerical Renormalization Group and Non--Crossing Approximation
• Pedestrian Approach to the Two-Channel Kondo Model
• Scaling theory of the Kondo screening cloud
• Negativity as the Entanglement Measure to Probe the Kondo Regime in the Spin-Chain Kondo Model
• Observation of the Kondo Screening Cloud of Micron Lengths
• Universality of the Kondo effect in quantum dots with ferromagnetic leads
• Controlling the Kondo Effect in CoCu_n Clusters Atom by Atom
• Transition from overscreening to underscreening in the multichannel Kondo model: exact solution at large N
• Kondo effect in three-dimensional Dirac and Weyl systems
• The Screening Cloud in the k-Channel Kondo Model: Perturbative and Large-k Results
• On the Kondo effect in carbon nanotubes at half halfing
• Quantum Impurity Entanglement
• Real-space renormalization group flow in quantum impurity systems: local moment formation and the Kondo screening cloud
• Kondo screening cloud effects in mesoscopic devices
• Heavy quark dynamics for charm and bottom flavor on Fermi surface at zero temperature
• Spectral function of the Kondo model in high magnetic fields
• QCD Kondo effect: quark matter with heavy-flavor impurities
• Kondo effect and non-Fermi liquid behavior in Dirac and Weyl semimetals
• Topological interpretation of Luttinger theorem
• Schwinger Boson approach to the fully screened Kondo model
• Macroscopic Quantum Entanglement of a Kondo Cloud at Finite Temperature
• Tunable Kondo physics in a carbon nanotube double quantum dot
• Conserving Diagrammatic Approximations for Quantum Impurity Models: NCA and CTMA
• Unveiling the internal entanglement structure of the Kondo singlet
• Kondo effect in charm/bottom nuclei
• Spatially dependent Kondo effect in Quantum Corrals
• Local susceptibility and Kondo scaling in the presence of finite bandwidth
• Impurity entanglement entropy in Kondo systems from conformal field theory
• On The Multichannel Kondo Model"
• Fermi/non-Fermi mixing in SU($N$) Kondo effect
• Finite-size scaling for the S=1/2 Heisenberg Antiferromagnetic Chain
• Kondo effect of ${\bar{D}}_s$ and ${\bar{D}}_s^{\ast }$ mesons in nuclear matter
• Bosonization Approach to the One-Dimensional Kondo Lattice Model at Half Filling: Reexamination
• Detecting Kondo Entanglement by Electron Conductance
• A non-perturbative field theory approach for the Kondo effect: Emergence of an extra dimension and its implication for the holographic duality conjecture
• Scaling theory for Mott-Hubbard transitions
• Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis
• Intermediate coupling fixed point study in the overscreened regime of generalized multichannel SU(N) Kondo models
• Holographic unitary renormalization group for correlated electrons -- I: a tensor network approach
• Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality
• Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid
• Origin of Topological Order in a Cooper Pair Insulator

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