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

We study the quantum phase transition of an $S=1\mathrm{/}2$ anisotropic $\alpha$ $(\equiv J_z\mathrm{/}{J}_{xy})$ 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 $N\le 36$ sites. The $N$ dependence of the Binder ratios reveals that the classical 120${}^{\circ }$ N'{e}el state occurs for $\alpha \lesssim 0.55$, whereas a critical collinear state occurs for $1\mathrm{/}\alpha \lesssim 0.6$. This result is at odds with a widely-held belief that the ground state of a Heisenberg antiferromagnet is the 120${}^{\circ }$ N'{e}el state, but it also provides a possible mechanism explaining experimentally observed spin liquids.