{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"265e34f7aec8144fda728c9fa392dc7bf363d78300e26aae029c31353b9fea47","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"21108a10ff774c918b5c9e861372afb11ba4176e612db3347a45662f294fb170","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.quantum-spin-gaps.half-integer-gapless","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Chains of half-integer spins are expected to have no energy gap. A general theorem allows either no gap or several ground states, and only the spin-1/2 case is solved exactly.","posed_since":"1983","precise":"For $H = \\sum_i S_i . S_{i+1}$ with $S = 3/2$ (or any half-integer $S \\ge 3/2$), prove that $E_1(L) - E_0(L) \\to 0$ as $L \\to \\infty$ with a unique ground state, or equivalently exclude dimerization. The Lieb-Schultz-Mattis theorem (and Affleck-Lieb extension) gives gapless or degenerate. Answer: a proof.","problem_ref":null,"references":"","settled_by":"A proof that the $S = 3/2$ chain is gapless with a unique ground state.","status_note":"","title":"Gaplessness of half-integer spin Heisenberg chains with $S \\ge 3/2$","topic_ref":"2277c2056f9b4652a96eb984886b4114703ad1bdf3de5eaf3cbb73c0aab421ae"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"fcf9004d01e8627a8fa0db177c59499e35d1c6f148a7dde5ec76465776f77be4","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"dbece18c71fac9515b86a4a18283eaf842dbdb773b4fb998da91687a16dd0f46","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"mHYcc2nEc6hgORRIRGj4XmnQmIxCJfCYsgFYCkajCioGKw3D5QX-UKqACimHJOFMM5FHkHbVNcXlkG5NttMAAg"},"schema":"pubphys.envelope/1"},"record_hash":"fcf9004d01e8627a8fa0db177c59499e35d1c6f148a7dde5ec76465776f77be4","leaf_index":1654}