Entanglement and separability in continuum Rokhsar-Kivelson states
Bibliographic record
Abstract
We study a vast family of continuum Rokhsar-Kivelson (RK) states, which have their ground state encoded by a local quantum field theory. These describe certain quantum magnets, and are also important in quantum information. We prove the separability of the reduced density matrix of two disconnected subsystems, implying the absence of entanglement between the two subsystems---a stronger statement than the vanishing of logarithmic negativity. As a particular instance, we investigate the case where the ground state is described by a relativistic boson, which is relevant for certain magnets or Lifshitz critical points with dynamical exponent $z=2$, and we propose nontrivial deformations that preserve their RK structure. Specializing to 1D systems, we study a deformation that maps the ground state to the quantum harmonic oscillator, leading to a gap for the boson. We study the resulting correlation functions, and find that cluster decomposition is restored. We analytically compute the $c$ function for the entanglement entropy along a renormalization group flow for the wavefunction, which is found to be strictly decreasing as in CFTs. Finally, we comment on the relations to certain stoquastic quantum spin chains. We show that the Motzkin and Fredkin chains possess unusual entanglement properties not properly captured by previous studies.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".