{"paper":{"title":"The Localization Dichotomy for gapped periodic quantum systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math-ph","math.MP"],"primary_cat":"cond-mat.mes-hall","authors_text":"A. Pisante, D. Monaco, G. Panati, S. Teufel","submitted_at":"2016-12-30T18:45:18Z","abstract_excerpt":"We investigate the localization properties of gapped periodic quantum systems, modeled by a periodic or covariant family of projectors, as e.g. the orthogonal projectors on the occupied orbitals at fixed crystal momentum for a gas of non-interacting electrons. We prove a general localization dichotomy for dimension $d\\leq 3$: either the system is topologically trivial i.e. all the Chern numbers vanish, or any arbitrary choice of composite Wannier functions yields an infinite expectation value for the squared position operator. Equivalently, in the topologically non-trivial phase, the localizat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09557","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"}