  We explore low temperature properties of quantum triangular Heisenberg
antiferromagnets in two dimension in the vicinity of the quantum phase
transition at zero temperature. Using the effective field theory described by
the $SO(3)\times SO(2)/SO(2)$ matrix Ginzburg-Landau-Wilson model and the
non-perturbative renormalization group method, we clarify how quantum and
thermal fluctuations affect long-wavelength behaviors in the parameter region
where the systems exhibit a fluctuation-driven first order transition to a
long-range ordered state. We show that at finite temperatures the crossover
from a quantum $\phi^6$ theory to a renormalized two-dimensional classical
nonlinear sigma model region appears, and in this crossover region, massless
fluctuation modes with linear dispersion a la spin waves govern low-energy
physics. Our results are in good agreement with the recent experimental
observations for the two-dimensional triangular Heisenberg spin system,
NiGa$_2$S$_4$.
