{"paper":{"title":"Translation Groups for arbitrary Gauge Fields in Synthetic Crystals with real hopping amplitudes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.other","cond-mat.soft"],"primary_cat":"cond-mat.mes-hall","authors_text":"Marco Marciani","submitted_at":"2025-08-11T20:39:25Z","abstract_excerpt":"The Cayley-crystals introduced in [F. R. Lux and E. Prodan, Annales Henri Poincar\\'e 25(8), 3563 (2024)] are a class of lattices endowed with a Hamiltonian whose translation group $G$ is generic and possibly non-commutative. We show that these systems naturally realize the generalization of the so-called magnetic translation groups to arbitrary discrete gauge groups. A one-body dynamics emulates that of a particle carrying a superposition of charges, each coupled to distinct static gauge-field configuration. The possible types of gauge fields are determined by the irreducible representations o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.08461","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/2508.08461/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"}