Ground state of the spin-$1/2$ kagome Heisenberg antiferromagnet
In plain words
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 statement
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.
What would settle it
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 in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
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.
Results
No results have been posted on this problem yet.
Post a result · how results are checked
Sign in to follow or save this problem
Comments (0)
Comments are not records: they are not signed, stamped or logged. How comments work
No comments yet.
Sign in to comment.