Dissecting Kitaev Spin Liquid into Collective Patterns of Spin Coupling Bonds in Real Space

How to characterize the topological order of quantum spin liquids remains a long-standing theoretical challenge. In this work, we employ the pattern decomposition method to analyze the fine structure of the Kitaev spin liquid on a finite honeycomb lattice. The Kitaev Hamiltonian decomposes into six sub-Hamiltonians whose weight factors form periodic patterns under unit cell translations. Correspondingly, the eigenstates of the Kitaev spin liquid are partitioned into six degenerate subspaces, unveiling the ordered structure of the spin liquid state. The critical point of the topological phase transition from a gapped to a gapless phase is identified through the sub-Hamiltonians. This Hamiltonian dissection approach reveals the fine structure of the Kitaev spin liquid and offers a promising platform for the quantum simulation of spin liquids.