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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 calculationsendowed with a density-matrix-renormalization-group solver, we reveal thequantum phases selected by quantum fluctuations from the massively degenerateclassical ground-state manifold. The magnetization process up to saturationreflects three different magnetic phases. The low- and high-field phases havestrong nematic nature, and especially the latter is found only via a nontrivialreconstruction of symmetry generators from the standard spin and quadrupolardescription. We also perform a semiclassical Monte Carlo simulations to showthat thermal fluctuations prefer the same three phases as well. Moreover, wefind that exotic topological phase transitions driven by the binding-unbindingof fractional (half-)vortices take place, due to the nematicity of the low- andhigh-field phases. Possible experimental realization with alkaline-earth-likecold atoms is also discussed.

Quantum and Thermal Phase Transitions of the Triangular SU(3) Heisenberg Model under Magnetic Fields