{"paper":{"title":"Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.mes-hall","quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Gautam Nambiar, Maissam Barkeshli, Naren Manjunath, Yuxuan Zhang","submitted_at":"2022-11-16T19:00:00Z","abstract_excerpt":"We show how to define a quantized many-body charge polarization $\\vec{\\mathscr{P}}$ for (2+1)D topological phases of matter, even in the presence of non-zero Chern number and magnetic field. For invertible topological states, $\\vec{\\mathscr{P}}$ is a $\\mathbb{Z}_2 \\times \\mathbb{Z}_2$, $\\mathbb{Z}_3$, $\\mathbb{Z}_2$, or $\\mathbb{Z}_1$ topological invariant in the presence of $M = 2$, $3$, $4$, or $6$-fold rotational symmetry, lattice (magnetic) translational symmetry, and charge conservation. $\\vec{\\mathscr{P}}$ manifests in the bulk of the system as (i) a fractional quantized contribution of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.09127","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/2211.09127/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"}