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It is well known that magnons, elementary excitations in a magnetic material,behave as bosons when their density is low. We study how the bosonic characterof magnons is governed by the amount of a multipartite entanglement in thevacuum state on which magnons are excited. We show that if the multipartiteentanglement is strong, magnons cease to be bosons. We also consider someexamples, such as ground states of the Heisenberg ferromagnet and thetransverse Ising model, the condensation of magnons, the one-way quantumcomputer, and Kitaev's toric code. Our result provides insights into thequantum statistics of elementary excitations in these models, and into thereason why a non-local transformation, such as the Jordan-Wignertransformation, is necessary for some many-body systems.

Vacuum entanglement governs the bosonic character of magnons