{"paper":{"title":"Sub-ballistic operator growth in spin chains with heavy-tailed random fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"Christopher L. Baldwin","submitted_at":"2024-09-25T18:00:25Z","abstract_excerpt":"We rigorously prove that in nearly arbitrary quantum spin chains with power-law-distributed random fields, namely such that the probability of a field exceeding $h$ scales as $h^{-\\alpha}$, it is impossible for any operator evolving in the Heisenberg picture to spread with dynamical exponent less than $1/\\alpha$. In particular, ballistic growth is impossible for $\\alpha < 1$, diffusive growth is impossible for $\\alpha < 1/2$, and any finite dynamical exponent becomes impossible for sufficiently small $\\alpha$. This result thus establishes a wide family of models in which the disorder provably "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.17242","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.17242/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":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}