{"paper":{"title":"Quantum Spin Chains and Symmetric Functions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"quant-ph","authors_text":"Anupam Prakash, Marcos Crichigno","submitted_at":"2024-04-05T18:00:02Z","abstract_excerpt":"We consider the question of what quantum spin chains naturally encode in their Hilbert space. It turns out that quantum spin chains are rather rich systems, naturally encoding solutions to various problems in combinatorics, group theory, and algebraic geometry. In the case of the XX Heisenberg spin chain these are given by skew Kostka numbers, skew characters of the symmetric group, and Littlewood-Richardson coefficients. As we show, this is revealed by a fermionic representation of the theory of \"quantized\" symmetric functions formulated by Fomin and Greene, which provides a powerful framewor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.04322","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/2404.04322/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"}