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Resonant inelastic x-ray scattering (RIXS) at the oxygen $K$-edge hasrecently accessed multi-spinon excitations in the one-dimensionalantiferromagnet (1D-AFM) \sco, where four-spinon excitations are resolvedseparately from the two-spinon continuum. This technique, therefore, providesnew opportunities to study fractionalized quasiparticle excitations in doped1D-AFMs. To this end, we carried out exact diagonalization studies of the doped$t$-$J$ model and provided predictions for oxygen $K$-edge RIXS experiments ondoped 1D-AFMs. We show that the RIXS spectra are rich, containing distinct two-and four-spinon excitations, dispersive (anti)holon excitations, andcombinations thereof. Our results highlight how RIXS complements inelasticneutron scattering experiments by accessing additional charge and spincomponents of fractionalized quasiparticles.

Multi-spinon and holon excitations probed by resonant inelastic x-ray scattering on doped one-dimensional antiferromagnets