  We introduce an entanglement entropy analysis to quantitatively identify the
confinement and deconfinement of the spinons in the spin excitations of quantum
magnets. Our proposal is implemented by the parton construction of a
honeycomb-lattice antiferromagnet exhibiting high-energy anomalous spectra. To
obtain the quasiparticles of spin excitations for entanglement entropy
calculations, we develop an effective Hamiltonian using the random phase
approximation. We elaborate quantitatively the deconfinement-to-confinement
transition of spinons in the anomalous spectra with the increase of the Hubbard
interaction, indicating the avoided fractionalization of magnons in the strong
interaction regime. Meanwhile, the Higgs mode at the {\Gamma}0 point is
fractionalized into four degenerate spinon pairs, although it appears as a
sharp well-defined peak in the spectra. Our work extends our understanding of
the deconfinement of the spinon and its coexistence with the magnon in quantum
magnets.

Strongly Correlated Electrons