By using the tensor-network state algorithm, we study a spin-orbital model with $\mathrm{SU}\left(2\right)\times \mathrm{SU}\left(2\right)\times \mathrm{U}\left(1\right)$ symmetry on the triangular lattice. This model was proposed to describe some triangular $d^1$ materials and was argued to host a spin-orbital liquid ground state. In our work the trial wave function of its ground state is approximated by an infinite projected entangled simplex state and optimized by the imaginary-time evolution. Contrary to the previous conjecture, we find that the two SU(2) symmetries are broken, resulting in a stripe spin-orbital order with the same magnitude $m=0.085\left(10\right)$. This value is about half of that in the spin-1/2 triangular Heisenberg antiferromagnet. Our result demonstrates that although the long-sought spin-orbital liquid is absent in this model the spin-orbital order is significantly reduced due to the enhanced quantum fluctuation. This suggests that high-symmetry spin-orbital models are promising in searching for exotic states of matter in condensed-matter physics.

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• Frustrated magnetism
• Spin-orbit coupling
• Antiferromagnets
• Triangular lattice
• Heisenberg model
• Spin lattice models
• Tensor network methods