Cornering Gapless Quantum States via Their Torus Entanglement
Bibliographic record
Abstract
The entanglement entropy (EE) has emerged as an important window into the structure of complex quantum states of matter. We analyze the universal part of the EE for gapless systems on tori in 2D and 3D, denoted by χ. Focusing on scale-invariant systems, we derive general nonperturbative properties for the shape dependence of χ and reveal surprising relations to the EE associated with corners in the entangling surface. We obtain closed-form expressions for χ in 2D and 3D within a model that arises in the study of conformal field theories (CFTs), and we use them to obtain Ansätze without fitting parameters for the 2D and 3D free boson CFTs. Our numerical lattice calculations show that the Ansätze are highly accurate. Finally, we discuss how the torus EE can act as a fingerprint of exotic states such as gapless quantum spin liquids, e.g., Kitaev's honeycomb model.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".