Impurity entanglement in the<i>J</i>–<i>J</i><sub>2</sub>–δ quantum spin chain
Bibliographic record
Abstract
The contribution to the entanglement of an impurity attached to one end of a J – J 2 –δ quantum spin chain ( S = 1/2) is studied. Two different measures of the impurity contribution to the entanglement have been proposed: the impurity entanglement entropy S imp and the negativity . The first, S imp , is based on a subtractive procedure where the entanglement entropy in the absence of the impurity is subtracted from results with the impurity present. The other, , is the negativity of a part of the system separated from the impurity and the impurity itself. In this paper we compare the two measures and discuss their similarities and the differences between them. In the J – J 2 –δ model it is possible to perform very precise variational calculations close to the Majumdar–Ghosh point ( J 2 = J /2 and δ = 0) where the system is gapped with a dimerized ground state. We describe in detail how such calculations are done and how they can be used to calculate as well as S imp for any impurity coupling J K . We then study the complete crossover in the impurity entanglement as J K is varied between 0 and 1 close to the Majumdar–Ghosh point. In particular, we study the impurity entanglement when a staggered nearest neighbour interaction proportional to δ is introduced. In this case we observe a very rapid reduction in the impurity entanglement as δ is increased.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".