{"paper":{"title":"Emergent Wigner-Dyson Statistics and Self-Attention-Based Prediction in Driven Bose-Hubbard Chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A self-attention algorithm on driven Bose-Hubbard chains produces many-body spectra whose level statistics sit between the Gaussian Symplectic and Gaussian Unitary ensembles according to the ratio U/J.","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Chen-Huan Wu","submitted_at":"2022-08-02T08:15:14Z","abstract_excerpt":"We propose an algorithm based on modulable hidden variables and adaptive step lengths, inspired by heuristic statistical physics and the replica method, to study the effect of mutual correlations and the emergent Wigner-Dyson distribution in a driven many-body system.\n  Specifically, we apply this method to the driven Bose-Hubbard chain to illustrate the competition between coherent driving, hopping, and on-site interactions.\n  Unlike the asymptotic high-dimensional statistics regime in random systems, here the randomness emerges dynamically from the interplay between the driving field $F$ and"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The resulting system follows statistics intermediate between the Gaussian Symplectic Ensemble (GSE) and Gaussian Unitary Ensemble (GUE), contingent on the ratio U/J. Our algorithm allows for the automatic optimization and prediction of the resulting many-body spectrum to arbitrary accuracy, revealing non-Fermi liquid-like behavior in the strongly interacting bosonic phase.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the Gaussian-based self-attention mapping to high-dimensional feature space, with flavor number O(M) set by the local Kerr potential difference 1/2 U, faithfully reproduces the chaotic many-body spectrum and level statistics without requiring explicit verification against exact diagonalization on accessible system sizes.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A replica-inspired algorithm with Gaussian self-attention predicts many-body spectra in driven Bose-Hubbard chains and reports statistics intermediate between GSE and GUE depending on U/J.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A self-attention algorithm on driven Bose-Hubbard chains produces many-body spectra whose level statistics sit between the Gaussian Symplectic and Gaussian Unitary ensembles according to the ratio U/J.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a0e7dd3b9f8a10c7f08f974af662c248878c881ed0dea7e7a4331513209311b4"},"source":{"id":"2208.01303","kind":"arxiv","version":11},"verdict":{"id":"0449e7f8-a365-49fd-a9f3-d49097288a30","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-24T11:10:49.185560Z","strongest_claim":"The resulting system follows statistics intermediate between the Gaussian Symplectic Ensemble (GSE) and Gaussian Unitary Ensemble (GUE), contingent on the ratio U/J. Our algorithm allows for the automatic optimization and prediction of the resulting many-body spectrum to arbitrary accuracy, revealing non-Fermi liquid-like behavior in the strongly interacting bosonic phase.","one_line_summary":"A replica-inspired algorithm with Gaussian self-attention predicts many-body spectra in driven Bose-Hubbard chains and reports statistics intermediate between GSE and GUE depending on U/J.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the Gaussian-based self-attention mapping to high-dimensional feature space, with flavor number O(M) set by the local Kerr potential difference 1/2 U, faithfully reproduces the chaotic many-body spectrum and level statistics without requiring explicit verification against exact diagonalization on accessible system sizes.","pith_extraction_headline":"A self-attention algorithm on driven Bose-Hubbard chains produces many-body spectra whose level statistics sit between the Gaussian Symplectic and Gaussian Unitary ensembles according to the ratio U/J."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.01303/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"0b06c911293140b55560270516e50ed87e35945ab4b06896ee647511b69110cc"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}