Ground state of the spin-$1/2$ pyrochlore Heisenberg antiferromagnet
In plain words
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.
Precise statement
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.
What would settle it
Controlled 3D numerics (PEPS, neural-network states or DMRG on large clusters) that agree on the extrapolated dimer order parameter.
Status in the literature
Unverified 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).