Operator growth in disordered spin chains: Indications for the absence of many-body localization
Bibliographic record
Abstract
We consider the spreading of a local operator A in one-dimensional many-body systems with Hamiltonian H by calculating the k -fold commutator [ H , [ H , [ . . . , [ H , A ] ] ] ] . We derive bounds for the operator norm of this commutator in free and interacting systems with and without disorder thus directly connecting the with questions of localization. We analytically show, in particular, that an almost-factorial growth of the operator norm—as recently proven for the random Ising model and strongly suggested here to also hold for the Heisenberg model with random fields—is inconsistent with an exponential localization of A . Assuming there exists a quasilocal unitary U which maps H onto an effective Hamiltonian H ̃ = U H U † = ∑ n E n τ n z + ∑ i , j J i j τ i z τ j z + ⋯ , we show that A ̃ = U A U † is a quasilocal operator which, in contrast to the Anderson case, indeed in the general many-body case, leading to an almost-factorial growth of the commutator norm. Therefore, either the unitary U in many-body systems with maximal norm growth does not exist, and such systems are always ergodic, or unusual nonergodic phases described by H ̃ exist which violate the operator growth hypothesis and in which local operators spread over the entire lattice, implying that transport will eventually set in. To investigate this issue further, we concentrate on the chain with random magnetic fields. We analytically and symbolically verify our general results for the noninteracting Anderson and Aubry-André models. For the case, the symbolic calculations are consistent with a maximal norm growth. Furthermore, we find no indication of a weakened exponential localization of A , expected for strong disorder and low commutator orders if the unitary U does exist. Finally, we study the differences between the interacting and noninteracting cases when trying to perturbatively construct U by consecutive Schrieffer-Wolff transformations. While it is straightforward to show that this construction converges in the Anderson case, we find no indications for a convergence in the interacting case, suggesting that U does not exist and that many-body localization is absent.
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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 | 0.004 |
| 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 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".