Hints of possible spin-liquid state in the spin-1/2 triangular-lattice Heisenberg antiferromagnet

We calculate magnetic susceptibility of the triangular-lattice quantum antiferromagnet in the correlated paramagnet regime and reveal surprising microscopic correspondence between quantum and classical models at all accessible temperatures $T>0.375J$. Namely, we observe a perfect match between the quantum static (zero Matsubara frequency) response $\chi (r)$, where $r$ is the spatial coordinate, and its classical counterpart calculated at temperature $T_{cl}(T)$. The correspondence curve is rather featureless and smoothly extrapolates to a finite value of $T_{cl} = 0.28J$ when $T/J \to 0$. If this extrapolation indeed holds true, then finite value of $T_{cl}(0)$ implies that spins are not ordered in the ground state and form a spin liquid. Existing numerical evidence would $not$ be in contradiction with the spin liquid state because the spin correlation length for the classical Heisenberg model at $T_{cl} \approx 0.28J$ is $>1000$ lattice periods and simulations dealing with small system sizes $L< 10$ would misidentify the ground state as ordered. Our results are based on the high-order skeleton Feynman diagrams within the fermionization framework.