Spin diffusion and the anisotropic spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mstyle scriptlevel="1"><mml:mfrac bevelled="false"><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mstyle></mml:math>Heisenberg chain
Bibliographic record
Abstract
Measurements of the spin-lattice relaxation rate $1∕{T}_{1}$ by nuclear magnetic resonance for the one-dimensional Heisenberg antiferromagnet ${\mathrm{Sr}}_{2}\mathrm{Cu}{\mathrm{O}}_{3}$ have provided evidence for a diffusionlike contribution at finite temperature and small wave vector. By analyzing real-time data for the auto- and nearest-neighbor spin-spin correlation functions obtained by the density-matrix renormalization group I show that such a contribution indeed exists for temperatures $T>J$, where $J$ is the coupling constant, but that it becomes exponentially suppressed for $T⪡J$. I present evidence that the frequency dependence of $1∕{T}_{1}$ in the Heisenberg case is smoothly connected to that in the free fermion case where the exponential suppression of the diffusionlike contribution is easily understood.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".