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

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

2004-06-28

arxiv.org/abs/quant-ph/0406202v3

Phys.Lett. A 337, 22 (2005)

Physics

Quantum Physics

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

Scientific paper

10.1016/j.physleta.2005.01.060

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.

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