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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.

  1. Is it gapped or gapless overall? The spin gap? The charge gap?

  2. What is the emergent gauge structure? Z2, U(1), SU(2), etc?

  3. What are the anyons? Gapped or gapless?

  4. 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.

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  • $\begingroup$ Are you asking about Herbertsmithite or about the kagome Heisenberg model? $\endgroup$
    – Norbert Schuch
    Commented Nov 15, 2016 at 10:11

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As you already mentioned, some features of Herbertsmithite are still highly controversial, especially concerning the gap. As far as I know also the question if it is a $U(1)$ or $Z_2$ SL is not settled yet. A good overview with some references can be found in Sec. 7.3.4 in a recent review.1

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