  We study the quantum phase transition of an $S=1/2$ anisotropic $\alpha$
$(\equiv J_z/J_{xy})$ 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$^{\circ}$ N\'{e}el state occurs for $\alpha \lesssim 0.55$, whereas a
critical collinear state occurs for $1/\alpha \lesssim 0.6$. 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.
