{"paper":{"title":"Asymptotic lower bound for the gap of Hermitian matrices having ergodic ground states and infinitesimal off-diagonal elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"C. Presilla, M. Ostilli","submitted_at":"2015-12-27T20:14:51Z","abstract_excerpt":"Given a $M\\times M$ Hermitian matrix $\\mathcal{H}$ with possibly degenerate eigenvalues $\\mathcal{E}_1 < \\mathcal{E}_2 < \\mathcal{E}_3< \\dots$, we provide, in the limit $M\\to\\infty$, a lower bound for the gap $\\mu_2 = \\mathcal{E}_2 - \\mathcal{E}_1$ assuming that (i) the eigenvector (eigenvectors) associated to $\\mathcal{E}_1$ is ergodic (are all ergodic) and (ii) the off-diagonal terms of $\\mathcal{H}$ vanish for $M\\to\\infty$ more slowly than $M^{-2}$. Under these hypotheses, we find $\\varliminf_{M\\to\\infty} \\mu_2 \\geq \\varlimsup_{M\\to\\infty} \\min_{n} \\mathcal{H}_{n,n}$. This general result tu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08271","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}