Energy dependence of localization with interactions and disorder: The generalized inverse participation ratio of an ensemble of two-site Anderson-Hubbard systems
Bibliographic record
Abstract
After Anderson's prediction of disorder-induced insulating behavior, extensive work found no singularities in the density of states of localized systems. However, Johri and Bhatt [Phys. Rev. Lett. 109, 076402 (2012) and Phys. Rev. B 86, 125140 (2012)] recently uncovered the existence of a nonanalyticity in the density of states near the band edge of noninteracting systems with bounded disorder, in an energy range outside that captured by previous work. Moreover, this feature marks the boundary of an energy range in which the localization is sharply suppressed. Given strong current interest in the effect of interactions on disordered systems, we explore here the effect of a Hubbard $U$ interaction on this behavior. We find that in ensembles of small systems a cusp in the density of states persists and continues to be associated with a sharp suppression of the localization. We explore the origins of this behavior and discuss its connection with many-body localization.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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) | 0.000 | 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 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".