Bibliographic record
Abstract
Motivated by the recent developments of quantum many-body chaos, characterizing how an operator grows and its complexity in the Heisenberg picture has attracted a lot of attentions.In this work, we study the operator growth problem in a many-body localization (MBL) system from a recently proposed Lanczos algorithm perspective.Using the Krylov basis, the operator growth problem can be viewed as a single particle hopping problem on a semi-infinite chain with the hopping amplitudes given by the Lanczos coefficients.We find that, in the MBL phase, the Lanczos coefficients scales ∼ n/ ln(n) asymptotically, same as in the ergodic phase, but with an additional even-odd alteration and effective randomness.Extrapolating the Lanczos coefficients to the thermodynamic limit, we study the spectral function and also find that the corresponding single-particle problem is localized for both unextrapolated and extrapolated Lanczos coefficients, resulting in a bounded "Krylov complexity" in time.For the MBL phenomenological model, the Lanczos coefficients also have an even-odd alteration, but approaching to constants asymptotically.We also find that the Krylov complexity grows linearly in time for the MBL phenomenological 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) | 0.001 | 0.001 |
| 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.103 | 0.002 |
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; both teacher heads agree on what is shown here.
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".