Description
We give an exact form of the density matrix for the spin-1/2 Kitaev spin liquid, expressed in terms of spin operators, and study the entanglement structure of the Kitaev spin liquid within the spin framework. We show that the density matrix is naturally organized by equivalence classes of string operators associated with the underlying gauge structure of the model. Using the explicit form of the density matrix, together with the exact Gauss law of the emergent gauge theory and the exact 1-form Wilson symmetry in the Kitaev model, we demonstrate the block-diagonal structure of the reduced density matrix, which gives rise to the extensive degeneracy in the entanglement spectrum. Furthermore, we explore subsystems with different numbers of lattice sites and topologies, revealing relationships between the entanglement spectrum and the subsystem fermion parity. Lastly, we briefly discuss the quantum magic of the Kitaev spin liquid and how the form of the density matrix implies its physical meaning.
Reference:
C.-C. Wang, Y.-P. Huang, and S. Yip, Phys. Rev. B 114, 305105