{"paper":{"title":"Asymmetric diffusion and the energy gap above the 111 ground state of the quantum XXZ model","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Fabio Martinelli, Pietro Caputo","submitted_at":"2001-06-26T10:02:49Z","abstract_excerpt":"We consider the anisotropic three dimensional XXZ Heisenberg ferromagnet in a cylinder with axis along the 111 direction and boundary conditions that induce ground states describing an interface orthogonal to the cylinder axis. Let $L$ be the linear size of the basis of the cylinder. Because of the breaking of the continuous symmetry around the $\\hat z$ axis, the Goldstone theorem implies that the spectral gap above such ground states must tend to zero as $L\\to \\infty$. In \\cite{BCNS} it was proved that, by perturbing in a sub--cylinder with basis of linear size $R\\ll L$ the interface ground s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0106523","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":""},"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"}