We investigate the quantum phases of higher-spin Kitaev models using tensor network methods. Our results reveal distinct valence-bond-ordered phases for spin-1, spin-$\frac{3}{2}$, and spin-2 models. In all cases, we find translational symmetry breaking with unit cells being tripled by forming valence-bond orders. However, these three phases are distinct, forming plaquette order, topological dimer order, and nontopological dimer order, respectively. Our findings are based on a cross-validation between variational two-dimensional tensor network calculations: an unrestricted exploration of symmetry-broken states versus the detection of symmetry breaking from cat-state behavior in symmetry-restricted states. The origin of different orders can also be understood from a theoretical analysis. Our Letter sheds light upon the interplay between topological and symmetry-breaking orders as well as their detection via tensor networks.

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• Projected entangled pair states
• Quantum spin liquid
• Topological order
• Valence bond solid
• Strongly correlated systems
• Kitaev model
• Tensor network methods