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 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 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.004 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.837 | 0.788 |
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".