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Spectral weight of doping-induced states in the 2D 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 $W_+(δ)\geδ$ ($δ$ denotes the total number of holes), in agreement with model predictions by Eskes {\it et al.} [Phys. Rev. Lett. {\bf 67}, 1035 (1991)]. However, if the cutoff energy is chosen to lie in the range of the pseudogap, $W_+(δ)$ remains much smaller than $δ$ and approximately saturates near $δ\approx 0.2...0.3$. The analysis of recent X-ray absorption spectroscopy data therefore depends crucially on the appropriate definition of the integration window.