Excitons and two-magnon Raman scattering of the strongly correlated systems ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_6$

We have solved two problems of strongly correlated electronic systems ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_6:$ (1) why the lowest-energy absorption peak has stronger oscillator strength than the higher-energy side in ${\mathrm{La}}_2{\mathrm{CuO}}_4$ while this relative magnitude is reversed in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_6,$ and (2) why, in both crystals, the two-magnon Raman scattering is observed strongly and resonantly enhanced largely around the high-energy absorption peak or shoulder, while not so appreciable on the low-energy side and around the strongest absorption peak with the lowest excitation energy. In order to treat these problems, an excitonic cluster model in which the bound and unbound states of the charge-transfer exciton are treated on equal footing is proposed to take into account the strong correlation effect of $\mathrm{Cu}\mathrm{}\left(3d\right)\mathrm{}$ electrons and the charge transfer of $\mathrm{O}\mathrm{}\left(2p\right)\mathrm{}$ electrons into the empty $\mathrm{Cu}\mathrm{}\left(3d\right)\mathrm{}$ orbitals.