Spectral weight of doping-induced states in the two-dimensional Hubbard model

The spectral weight of states induced in the Mott gap via hole doping in the two-dimensional Hubbard model is studied within cluster dynamical mean-field theory combined with finite-temperature exact diagonalization. If the cutoff energy is chosen to lie just below the upper Hubbard band, the integrated weight per spin is shown to satisfy W(+)(delta) >= delta (delta denotes the total number of holes), in agreement with model predictions by Eskes et al. [Phys. Rev. Lett. 67, 1035 (1991)]. However, if the cutoff energy is chosen to lie in the range of the pseudogap, W(+)(delta) remains much smaller than delta and approximately saturates near delta approximate to 0.2, ..., 0.3. The analysis of recent x-ray absorption spectroscopy data therefore depends crucially on the appropriate definition of the integration window.