Dispersion of the dielectric function of a charge-transfer insulator

Abstract

We study the problem of dielectric response in the strong-coupling regime of a charge-transfer insulator. The frequency and wave-number dependence of the dielectric function $\ensuremath{\varepsilon}(\mathbf{q},\ensuremath{\omega})$ and its inverse ${\ensuremath{\varepsilon}}^{\ensuremath{-}1}(\mathbf{q},\ensuremath{\omega})$ is the main object of consideration. We show that the problem, in general, cannot be reduced to a calculation within the Hubbard model, which takes into account only a restricted number of electronic states near the Fermi energy. The contribution of the rest of the system to the longitudinal response [i.e., to ${\ensuremath{\varepsilon}}^{\ensuremath{-}1}(\mathbf{q},\ensuremath{\omega})]$ is essential for the whole frequency range. With the use of the spectral representation of the two-particle Green's function we show that the problem may be divided into two parts: into the contributions of the weakly correlated subsystem and the Hubbard subsystem. For the latter we propose an approach that starts from the correlated paramagnetic ground state with strong antiferromagnetic fluctuations. We obtain a set of coupled equations of motion for the two-particle Green's function that may be solved by means of the projection technique. The solution is expressed by a two-particle basis that includes the excitonic states with electron and hole separated at various distances. We apply our method to the multiband Hubbard (Emery) model that describes layered cuprates. We show that strongly dispersive branches exist in the excitonic spectrum of the ``minimal'' Emery model ${(1/U}_{d}{=U}_{p}{=t}_{\mathrm{pp}}=0)$ and consider the dependence of the spectrum on finite oxygen hopping ${t}_{\mathrm{pp}}$ and on-site repulsion ${U}_{p}.$ The relationship of our calculations to electron-energy-loss spectroscopy is discussed.