A path integral ground state replica trick approach for the computation of entanglement entropy of dipolar linear rotors
Bibliographic record
Abstract
We calculate the second Rényi entanglement entropy for systems of interacting linear rotors in their ground state as a measure of entanglement for continuous rotational degrees of freedom. The entropy is defined in relation to the purity of a subsystem in a bipartite quantum system, and to compute it, we compare two sampling ensembles based on the path integral ground state (PIGS) formalism. This scheme centers on the replica trick and is aided by the ratio trick, both developed in this context by Hastings et al. [Phys. Rev. Lett. 104, 157201 (2010)]. We study a system composed of linear quantum rotors on a lattice in one dimension, interacting via an anisotropic dipole-dipole potential. The ground state second Rényi entropies estimated by PIGS are benchmarked against those from the density matrix renormalization group for various interaction strengths and system sizes. We find that the entropy grows with an increase in interaction strength, and for large enough systems, it appears to plateau near log(2). We posit that the limiting case of many strongly interacting rotors behaves akin to a lattice of two-level particles in a cat state, in which one naturally finds an entanglement entropy of log(2).
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 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".