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 $J-J_2-delta$ 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 N. 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, N, 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 similarities and differences between them. In the $J-J_2-\delta$ model it is possible to perform very precise variational calculations close to the Majumdar-Ghosh-point (J_2 = J / 2 and \delta = 0) where the system is gapped with a two-fold degenerate dimerized ground-state. We describe in detail how such calculations are done and how they can be used to calculate N as well as S_{imp} for any impurity-coupling J_K. We then study the complete cross-over 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 $\delta$ is introduced. In this case, the two-fold degeneracy of the ground-state is lifted leading to a very rapid reduction in the impurity entanglement as $\delta$ is increased.
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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 | 0.003 | 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".