  We study the quantum and thermal phase transition phenomena of the SU(3)
Heisenberg model on triangular lattice in the presence of magnetic fields.
Performing a scaling analysis on large-size cluster mean-field calculations
endowed with a density-matrix-renormalization-group solver, we reveal the
quantum phases selected by quantum fluctuations from the massively degenerate
classical ground-state manifold. The magnetization process up to saturation
reflects three different magnetic phases. The low- and high-field phases have
strong nematic nature, and especially the latter is found only via a nontrivial
reconstruction of symmetry generators from the standard spin and quadrupolar
description. We also perform a semiclassical Monte Carlo simulations to show
that thermal fluctuations prefer the same three phases as well. Moreover, we
find that exotic topological phase transitions driven by the binding-unbinding
of fractional (half-)vortices take place, due to the nematicity of the low- and
high-field phases. Possible experimental realization with alkaline-earth-like
cold atoms is also discussed.
