{"paper":{"title":"Sixteen-State Energy Mapping for First-Principles Four-Spin Ring Exchange: Validation on $La_2CuO_4$ and $SrFeO_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.str-el","quant-ph"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Peter Blaha, Xavier Rocquefelte","submitted_at":"2026-07-21T11:19:52Z","abstract_excerpt":"Four-spin ring (cyclic) exchange $J_{ring}$ is an essential ingredient of the Heisenberg spin Hamiltonian of cuprates and other square-lattice magnets, yet it has lacked the kind of direct, local first-principles extraction that the four-state method provides for bilinear exchange, $J$. We supply it by generalizing that method to a sixteen-state ($2^4$) scheme. Symmetry reduces the sixteen configurations to six or eight inequivalent energies, so the cost is modest. The derivation also shows that the conventional four-state magnetic coupling, $J$, is itself ring-renormalized, by $\\pm 2 J_{ring}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18986","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.18986/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"}