Variational wave functions for Sachdev-Ye-Kitaev models
Bibliographic record
Abstract
Given a class of q-local Hamiltonians, is it possible to find a simple variational state whose energy is a finite fraction of the ground-state energy in the thermodynamic limit? Whereas product states often provide an affirmative answer in the case of bosonic (or qubit) models, we show that Gaussian states fail dramatically in the fermionic case, such as for the Sachdev-Ye-Kitaev (SYK) models. This prompts us to propose a new class of wave functions for SYK models inspired by the variational coupled cluster algorithm. We introduce a static "(0+0)-dimensional" large-N field theory to study the energy, two-point correlators, and entanglement properties of these states. Most importantly, we demonstrate a finite disorder-averaged approximation ratio of r 0.62 between the variational and ground-state energy of the SYK model for q = 4. Moreover, the variational states provide an exact description of spontaneous symmetry breaking in a related two-flavor SYK 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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.001 | 0.001 |
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".