{"paper":{"title":"Winding number on 3D lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall"],"primary_cat":"hep-lat","authors_text":"Hiroshi Suzuki, Okuto Morikawa","submitted_at":"2024-12-05T05:41:12Z","abstract_excerpt":"We propose a simple numerical method which computes an approximate value of the winding number of a mapping from 3D torus~$T^3$ to the unitary group~$U(N)$, when $T^3$ is approximated by discrete lattice points. Our method consists of a ``tree-level improved'' discretization of the winding number and the gradient flow associated with an ``over-improved'' lattice action. By employing a one-parameter family of mappings from $T^3$ to $SU(2)$ with known winding numbers, we demonstrate that the method works quite well even for coarse lattices, reproducing integer winding numbers in a good accuracy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.03888","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/2412.03888/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"}