{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"43267d28723dabd69553f28119c78fc59f7f2772da3f871c3916d89dbf2c9843","created":"2026-10-03T07:17:59Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"19bc11bde91763327f9d907c5c17a07c029f28fc3574cf7f5abf11a587febc80","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"cm.frustrated-heisenberg.pyrochlore-heisenberg","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"The pyrochlore lattice, a three-dimensional network of corner-sharing tetrahedra, is the most frustrated common lattice in three dimensions. For spin-$1/2$ Heisenberg coupling it is unknown whether the ground state is a spin liquid or breaks a lattice symmetry.","posed_since":"","precise":"H = J sum_<ij> S_i . S_j, $S = 1/2$, $J > 0$, nearest neighbors on the pyrochlore lattice. Determine whether the ground state breaks lattice (inversion or translation) symmetry through valence-bond order or is a quantum spin liquid, and give the ground-state energy per site with error bars.","problem_ref":null,"references":"","settled_by":"Controlled 3D numerics (PEPS, neural-network states or DMRG on large clusters) that agree on the extrapolated dimer order parameter.","status_note":"A 2021 DMRG study reported inversion-symmetry breaking, a 2023 study argued for a spin liquid (arXiv:2311.11561), and a 2025 variational study found competing valence-bond crystals (arXiv:2509.13746).","title":"Ground state of the spin-$1/2$ pyrochlore Heisenberg 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