We study the magnon-like properties of the repulsively interacting spin-3/2 fermions in one-dimensional optical lattices at quarter filling. By means of the Holstein-Primakoff transformation performed on the spinor chain we obtain a spinless boson system described by an extended Bose-Hubbard model with a hole-like lowest band. The magnon model involves single, pair and correlated hopping between nearest neighbors beside the on-site and nearest neighbor interactions. The Mott-insulator phases of the spin-3/2 lattice fermions are mirrored with the magnon-like counterpart by analyzing several observables which should reveal these phases in state-of-the-art experiments. The numerical calculations are performed using the Exact Diagonalization and Matrix Product State formalism.
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