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We discuss the problem of a possible violation of the optical sum rule in the normal (non superconducting) state of strongly correlated electronic systems, using our recently proposed DMFT+Sigma approach, applied to two typical models: the hot - spot model of the pseudogap state and disordered Anderson - Hubbard model. We explicitly demonstrate that the general Kubo single band sum rule is satisfied for both models. However, the optical integral itself is in general dependent on temperature and characteristic parameters, such as pseudogap width, correlation strength and disorder scattering, leading to effective violation of the optical sum rule, which may be observed in the experiments.
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