{"paper":{"title":"Phase transition and split property in quantum spin chain","license":"","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Anilesh Mohari","submitted_at":"2005-05-11T09:56:10Z","abstract_excerpt":"In this exposition we investigate further the general methodology proposed in [Mo2] to study properties of the ground states of a translation invariant Hamiltonian for one lattice dimensional quantum spin chain $\\cla=\\otimes_{\\IZ}M_d$, where $M_d$ is the matrix of $d \\times d$ complex matrices. We introduce a notion of quantum detailed balance [Mo1] for a translation invariant state on $\\cla$ and prove that such a pure state is uniformly mixing [BR,Ma2] if and only if the lattice space correlation functions decay exponentially. Furthermore we also prove that a pure lattice symmetric, translati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0505035","kind":"arxiv","version":6},"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"}