Speaker
Description
We give an exact form of the density matrix of the spin-1/2 Kitaev spin liquid represented in terms of spin operators and study the entanglement properties of the Kitaev model within the spin framework. With the explicit form of the density matrix, plus the exact Gauss law of the emergent gauge theory and the exact 1-form Wilson symmetry in the Kitaev model, we demonstrate the existence of the underlying block-diagonal structure of the reduced density matrix, which gives rise to the extensive degeneracy in the entanglement spectrum. The block-diagonal structure is then proven to be responsible for the separability of the entanglement entropy into the gauge and matter parts. Furthermore, the method for applying our theory to cases with an odd number of lattice sites is also discussed. It also demonstrates a relation between the entanglement spectrum and the fermion parity, which is seldom mentioned in the literature.