{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"e79ded0999f37c9c16b903834d83d529c62b0709744965fe1d249df9b5c54718","created":"2026-10-03T07:18:01Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"3abe22fa36499c4364e8a91873c45486f90e51c826cdf14f858caee369461d06","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"cm.triangular-kagome-spin-liquids.kagome-heisenberg-ground-state","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"The simplest model of spins on the kagome lattice still has no agreed ground state. The two main candidates are a spin liquid with a small energy gap and one with no gap and Dirac-cone excitations (energy growing linearly with momentum).","posed_since":"","precise":"Model: H = J sum_<ij> S_i . S_j, $S = 1/2$, $J > 0$, nearest neighbors on the kagome lattice. Determine whether the thermodynamic-limit ground state is a gapped $Z2$ spin liquid (finite triplet gap $\\Delta_t$, topological entanglement entropy $\\ln 2$) or a gapless $U(1)$ Dirac spin liquid ($\\Delta_t\\sim 1/L$, power-law correlations). An answer gives $\\Delta_t/J$ extrapolated to infinite size with error bars, or a proof that it vanishes.","problem_ref":null,"references":"","settled_by":"Converged DMRG, PEPS or neural-network variational results on cylinders and tori with circumferences beyond 12 sites that agree on the extrapolated spin gap and entanglement scaling.","status_note":"DMRG from 2011 favored a gapped $Z2$ state; DMRG with flux insertion and PEPS studies from 2017 to 2019 favor the $U(1)$ Dirac state; no consensus as of 2026.","title":"Ground state of the spin-$1/2$ kagome Heisenberg 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