Kondo Screening Cloud Scaling: Impurity Entanglement and Magnetization
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arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911766634561536 |
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| author | Sørensen, Erik S. |
| author_facet | Sørensen, Erik S. |
| contents | The screening of an impurity spin in the Kondo model occurs over a characteristic length scale $ξ_K$, 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 $r/ξ_K$ rather than depending on $r$ and $ξ_K$ 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 $J_K'$. 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 $J_K'$ is varied, a precise determination of $ξ_K$ can then be obtained. The length scale, $ξ_K$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08547 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kondo Screening Cloud Scaling: Impurity Entanglement and Magnetization Sørensen, Erik S. Strongly Correlated Electrons The screening of an impurity spin in the Kondo model occurs over a characteristic length scale $ξ_K$, 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 $r/ξ_K$ rather than depending on $r$ and $ξ_K$ 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 $J_K'$. 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 $J_K'$ is varied, a precise determination of $ξ_K$ can then be obtained. The length scale, $ξ_K$, 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. |
| title | Kondo Screening Cloud Scaling: Impurity Entanglement and Magnetization |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2310.08547 |