{"paper":{"title":"Local Perturbations Perturb -Exponentially- Locally","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Marius Sch\\\"utz, Wojciech De Roeck","submitted_at":"2015-01-19T17:38:43Z","abstract_excerpt":"We elaborate on the principle that for gapped quantum spin systems with local interaction \"local perturbations [in the Hamiltonian] perturb locally [the ground state]\". This principle was established in [Bachmann et al. 2012], relying on the `spectral flow technique' or `quasi-adiabatic continuation' [Hastings 2004] to obtain locality estimates with sub-exponential decay in the distance to the spatial support of the perturbation. We use ideas of [Hamza et Al. 2009] to obtain similarly a transformation between gapped eigenvectors and their perturbations that is local with exponential decay. Thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04571","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":""},"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"}