{"paper":{"title":"Universal relation between the dispersion curve and the ground-state correlation length in 1D antiferromagnetic quantum spin systems","license":"","headline":"","cross_cats":["cond-mat.str-el"],"primary_cat":"cond-mat.stat-mech","authors_text":"K. Okunishi, N. Akutsu, T. Yamamoto, Y. Akutsu","submitted_at":"2001-07-02T03:06:59Z","abstract_excerpt":"We discuss an universal relation $\\epsilon(i\\kappa)=0$ with ${\\rm Re} \\kappa=1/\\xi$ in 1D quantum spin systems with an excitation gap, where $\\epsilon(k)$ is the dispersion curve of the low-energy excitation and $\\xi$ is the correlation length of the ground-state. We first discuss this relation for integrable models such as the Ising model in a transverse filed and the XYZ model. We secondly make a derivation of the relation for general cases, in connection with the equilibrium crystal shape in the corresponding 2D classical system. We finally verify the relation for the S=1 bilinear-biquadrat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0107021","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/cond-mat/0107021/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"}