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Recently, investigations of the quantum properties of an antiferromagnet in the spin wave approximation have identified the eigenstates as two-mode squeezed sublattice-magnon states. The uniform magnon states were shown to display a massive sublattice entanglement. Here we extend this idea and study the squeezing properties of all sublattice Fock states throughout the magnetic Brillouin zone. We derive the full statistics of the sublattice magnon number with wave number k in the ground state and show that sublattice magnons occur in pairs with opposite wave vectors, hence, resulting in entanglement of both modes. To quantify the degree of entanglement we apply the Duan-Giedke-Cirac-Zoller inequality and show that it can be violated for all modes. The degree of entanglement decreases towards the corners of the Brillouin zone. We relate the entanglement to measurable correlations of components of the Néel and the magnetization vectors, thus allowing one to experimentally test the quantum nature of the squeezed vacuum. The distinct k-space structure of the entanglement shows that the squeezed vacuum has a nonuniform shape that is revealed through the k-dependent correlators for the magnetization and the Néel vectors.

Dennis Wuhrer, Niklas Rohling, Wolfgang Belzig
Phys. Rev. B 105, 054406 (2022) [arXiv:2108.01942]