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

2004/06/30 by A. Hamma, R. Ionicioiu, P. Zanardi · 3 citations
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1016/j.physleta.2005.01.060

published as Phys.Lett. A 337, 22 (2005) · 4 pages, one fig, ReVTeX 4; updated to the published version

arxiv created 2005/02/28 · arxiv updated 2009/12/01

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 ρ_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.

Cited by

• Higher-form entanglement asymmetry and topological order
• Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model
• A graphical diagnostic of topological order using ZX calculus

Related

• Bipartite entanglement and entropic boundary law in lattice spin systems
• Geometric Entanglement Entropy on Projective Hilbert Space
• Topological Geometric Entanglement
• Geometric Phase in Kitaev Quantum Spin Liquid
• Entanglement entropy in lattice models with quantum metric