Range of thet-Jmodel parameters forCuO2planes: Experimental data constraints

The t-J-model effective hopping integral is determined from the three-band Hubbard model for the charge carriers in ${\mathrm{CuO}}_{2}$ planes. For this purpose the values of the superexchange constant J and the charge-transfer gap ${\mathit{E}}_{\mathrm{gap}}$ are calculated in the framework of the three-band model. The energies of the local states for added electron and hole are obtained from the systematic analytical reduction of the three-band model and their kinetic energy is found from the accurate variational approach using the t-J model. Fitting values of J and ${\mathit{E}}_{\mathrm{gap}}$ to the experimental data allows us to narrow the uncertainty region of the threeband model parameters. As a result, the t/J ratio of the t-J model is fixed in the range 2.4--2.7 for holes and 2.5--3.0 for electrons. This approach explains the formation of the Frenkel exciton and correctly describes the main features of the charge-transfer spectrum.