Kondo screening cloud scaling: impurity entanglement and magnetization
Bibliographic record
Abstract
Abstract 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 scale in experimental and numerical results is rather subtle. A consistent way to show the presence of the screening cloud is to demonstrate scaling in the spatial correlations in terms of the single variable, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>r</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>ξ</mml:mi> <mml:mi>K</mml:mi> </mml:msub> </mml:math> instead of the correlations 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>J</mml:mi> <mml:mi>K</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">′</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> . 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>J</mml:mi> <mml:mi>K</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">′</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> 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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".