Spectral properties of $CuO$ chains across a Hubbard to charge-transfer insulator crossover

We carry out extensive numerical calculations of the photoemission spectra, optical conductivity and resonant inelastic X-ray scattering (RIXS) Cu $L$ edge spectrum of a generalized two band model for $CuO$ chains by means of the time dependent density matrix renormalization group method. By varying the Hamiltonian parameters, we study the crossover from Hubbard to charge-insulator and characterize the spectral signatures of the two regimes. We compare our results with experiments on the single chain oxide Sr$_2$CuO$_3$.