Revision 1

Accepted · first revision · record

Title: Ground state of the spin-$1/2$ kagome Heisenberg antiferromagnet
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).
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.
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.
Kind: well-posed
Answer type: classification
References: (empty)
Literature status: contested
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.
Posed since: (empty)