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 $W_{+}\left(\delta \right)\ge \delta$ ($\delta$ 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, $W_{+}\left(\delta \right)$ remains much smaller than $\delta$ and approximately saturates near $\delta \approx 0.2,\dots ,0.3$. The analysis of recent x-ray absorption spectroscopy data therefore depends crucially on the appropriate definition of the integration window.

• Received 8 April 2010

DOI:https://doi.org/10.1103/PhysRevB.81.235133