What kind of spin liquids the Herbertsmithite is? Roughly it is a spin-1/2 Heisenberg model on the Kagome lattice with a coupling $J>0$.
It seems that there are long mismatches between the theory, the numerical simulations and the experiments.
Is it gapped or gapless overall? The spin gap? The charge gap?
What is the emergent gauge structure? Z2, U(1), SU(2), etc?
What are the anyons? Gapped or gapless?
Are there emergent boson or fermion particles? Gapped or gapless? Are there emergent photons? Gapped or gapless?
What kind of long-range entanglement patterns, etc.