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arXiv:2511.07415 · Physical Review Letters

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

Xing-Yu Zhang, Qi Yang, Philippe Corboz, Jutho Haegeman, Yuchi He

Published Jul 13, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the quantum phases of higher-spin Kitaev models using tensor network methods. Our results reveal distinct bond-ordered phases for spin-1, spin-$\tfrac{3}{2}$, 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 non-topological 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 work sheds light upon the interplay between topological and symmetry-breaking orders as well as their detection via tensor networks.

DOI
10.1103/7q31-xxsd

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We map out the ground state phase diagram of the spin-12\frac{1}{2}21​ isotropic Kekul\'e-Kitaev model on the honeycomb lattice in the presence of the Heisenberg exchange couplings. Our study relies on large-scale tensor network simulations based on a graph-based projected entangled pair state approach and simple tensor update in the thermodynamic limit. We find that, on top of the quantum spin liquid and conventional magnetically ordered phases which are typical of the Kitaev-Heisenberg model, the Kekul\'e-Heisenberg phase diagram hosts two plaquette valence bond solid (VBS) phases with vanishing magnetic order. While the VBS phases preserve the symmetries of the original Hamiltonian, they differ markedly from the Kitaev spin liquid by having decorated plaquette ordering which is distinguished by a plaquette order parameter.
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