Ground state entanglement and geometric entropy in the Kitaev's model

Abstract

We study the entanglement properties of the ground state in Kitaev's model. This is a two-dimensional spin system with a torus topology and nontrivial four-body interactions between its spins. For a generic partition $(A,B)$ of the lattice we calculate analytically the von Neumann entropy of the reduced density matrix ${\rho }_A$ in the ground state. We prove that the geometric entropy associated with a region $A$ is linear in the length of its boundary. Moreover, we argue that entanglement can probe the topology of the system and reveal topological order. Finally, no partition has zero entanglement and we find the partition that maximizes the entanglement in the given ground state.

4 pages, one fig, ReVTeX 4; updated to the published version

References in corpus (5)

• Entanglement versus Correlations in Spin Systems
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Entanglement in a second order quantum phase transition
• Entanglement in the stabilizer formalism

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