{"paper":{"title":"Finite-size criteria for spectral gaps in $D$-dimensional quantum spin systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Marius Lemm","submitted_at":"2019-02-19T16:55:46Z","abstract_excerpt":"We generalize the existing finite-size criteria for spectral gaps of frustration-free spin systems to $D>2$ dimensions. We obtain a local gap threshold of $\\frac{3}{n}$, independent of $D$, for nearest-neighbor interactions. The $\\frac{1}{n}$ scaling persists for arbitrary finite-range interactions in $\\mathbb Z^3$. The key observation is that there is more flexibility in Knabe's combinatorial approach if one employs the operator Cauchy-Schwarz inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07141","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"}