Figure 4: Raman spectra as a function of n.

(a) The B_1g Raman spectra for various values of n calculated using exact diagonalization of the Hubbard model on 18-site clusters (see Methods). The calculations are done with the same Hubbard model parameters as in Figs 1 and 2, and with a Lorentzian broadening HWHM=0.1t. Evolution of the spectral (‘bimagnon’) peak in the Raman spectra denoted by the black arrows (see Methods for identification of the ‘bimagnon’ peaks) in panel (a) together with the results from 16-site clusters (solid symbols). For the 18-site calculations, for example, the bimagnon peaks are obtained by fitting the spectra around the black arrow in panel (a) with Lorentzian functions. These results are compared with experiments (open symbols) obtained from Raman scattering on La_2−xSr_xCuO₄ (ref. 20) and Nd_2−xCe_xCuO₄ (ref. 21), and oxygen K-edge RIXS on La_2−xSr_xCuO₄ (ref. 36).