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Absence of a classical long-range order in $S=1/2$ Heisenberg antiferromagnet on triangular lattice

We study the quantum phase transition of an $S=1/2$ anisotropic $α$ $(\equiv J_z/J_{xy})$ Heisenberg antiferromagnet on a triangular lattice. We calculate the sublattice magnetization and the long-range helical order-parameter and their Binder ratios on finite systems with $N \leq 36$ sites. The $N$ dependence of the Binder ratios reveals that the classical 120$^{\circ}$ Néel state occurs for $α\lesssim 0.55$, whereas a critical collinear state occurs for $1/α\lesssim 0.6$. This result is at odds with a widely-held belief that the ground state of a Heisenberg antiferromagnet is the 120$^{\circ}$ Néel state, but it also provides a possible mechanism explaining experimentally observed spin liquids.