Topological and Trivial Valence-Bond Orders in Higher-Spin Kitaev Models

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-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.