Kondo Screening Cloud Scaling: Impurity Entanglement and Magnetization

Abstract

The screening of an impurity spin in the Kondo model occurs over a characteristic length scale ${\xi }_K$, that defines the size of the Kondo screening cloud or ``mist". The presence of such a length sc A consistent way to show the presence of the screening cloud is to demonstrate scaling in the spatial correlations depending on $r$, in terms of the single variable $r/{\xi }_K$ rather than depending on $r$ and ${\xi }_K$ separately. Here we study the paradigmatic one channel Kondo model using a spin chain representation, with an impurity spin at one end of the chain coupled with a strength $J_K^{\prime }$. Using Fermi liquid theory combined with numerical results, we obtain new high precision estimates of the non-universal terms in the entanglement entropy which leads to a verification of the expected non-integer ground-state degeneracy, $g$. This then allows us to study the impurity contribution to the entanglement in detail. If the impurity coupling $J_K^{\prime }$ is varied, a precise determination of ${\xi }_K$ can then be obtained. The length scale, ${\xi }_K$, is then shown to characterize the scaling of both the uniform and alternating part of a measure of the magnetization of part of an odd length chain with.

arXiv comment17 oages, 7 figures

References in corpus (29)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Entanglement Entropy and Quantum Field Theory
• Geometric and Renormalized Entropy in Conformal Field Theory
• The ITensor Software Library for Tensor Network Calculations
• New Trends in Density Matrix Renormalization
• Boundary effects in the critical scaling of entanglement entropy in 1D systems
• Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators
• Entanglement entropy in quantum impurity systems and systems with boundaries
• Entanglement and boundary critical phenomena
• 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
• The Screening Cloud in the k-Channel Kondo Model: Perturbative and Large-k Results
• Quantum Impurity Entanglement
• Theory of quantum impurities in spin liquids
• Entanglement entropy in the Ising model with topological defects
• Magnetic impurities in the honeycomb Kitaev model
• Entanglement structure of the two-channel Kondo model
• Neel order in doped quasi one-dimensional antiferromagnets
• Impurity Entanglement Entropy and the Kondo Screening Cloud
• Macroscopic Quantum Entanglement of a Kondo Cloud at Finite Temperature
• Kondo Effect in Spin Chains
• Edge Magnetic Field in the xxz Spin-1/2 Chain
• Magnetic Impurity as a Local Probe of the U(1) Quantum Spin Liquid with Spinon Fermi Surface
• Vacancy-induced spin texture in a one dimensional $S=1/2$ Heisenberg antiferromagnet
• A Kondo route to spin inhomogeneities in the honeycomb Kitaev model
• Universal Thermal Entanglement of Multichannel Kondo Effects
• Zero-mode entanglement across a conformal defect