Fig. 2.

Comparison between the experimental and calculated RIXS spectra at the oxygen K-edge. a, b Experimental RIXS spectra as a function of momentum transfer and energy transfer measured at the oxygen K-edge with an incident photon energy of ℏω_in = 528.6 eV (resonance B) (a) and at the copper L₃-edge from ref. ⁴ (b). c compares the O K-edge (blue) and Cu L₃-edge (magenta line) RIXS line cuts at q = 0. In the case of Cu L₃ data, there is a tailing contribution from higher energy dd excitations, which extends down to low energy transfer (see Supplementary Note 3). d displays the calculated oxygen K-edge spectra for ℏω_in = 500 meV. (This value optimizes the intensity of the four-spinon features, see Supplementary Note 5.) The excitation around 90 meV in the oxygen K-edge data is a phonon excitation not included in our model calculations. The modeled RIXS intensity was obtained from exactly diagonalizing a 22-site t−J chain with periodic boundary conditions and the elastic line has been removed from the data for clarity. e, and f show line cuts of the RIXS spectra at q = π/2a and q = 0, respectively. The experimental (theoretical) data are represented by the blue (red) solid lines. The intensity of the RIXS data are reported in arbitrary units (arb. units). The dotted and dashed white lines in a, b, and d indicate the boundaries of the two- and four-spinon continua, respectively (for more details on these boundaries see Supplementary Note 4)