Nature of the spin liquid in the triangular $J1-J2$ Heisenberg model
In plain words
Adding a weak second-neighbor coupling to the triangular-lattice Heisenberg model destroys its 120-degree magnetic order and produces a nonmagnetic phase. Whether this phase is a gapless Dirac spin liquid, a gapped spin liquid or a chiral state is unsettled.
Precise statement
Model: H = J1 sum_<ij> S_i . S_j + J2 sum_<<ij>> S_i . S_j, $S = 1/2$, triangular lattice, roughly $0.07 < J2/J1 < 0.15$. Determine the phase ($U(1)$ Dirac spin liquid, $Z2$ spin liquid, chiral spin liquid or valence-bond order) and its boundaries. An answer gives the classification with spin and singlet gaps extrapolated to infinite size.
What would settle it
Agreement of several unbiased methods (DMRG with flux insertion, PEPS, neural-network states) on extrapolated gaps and on the monopole and spinon spectrum.
Status in the literature
DMRG with flux insertion (Hu et al., PRL 2019) supports a Dirac spin liquid; other variational and tensor-network studies report gapped or ordered states.