Abstract
We investigate the experimentally observed anomalous softening of certain high-frequency oxygen bond-stretching modes during the insulator-metal transition via the underdoped phase in ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}.$ The calculations show that the screening processes producing the softening behavior are well described in terms of charge fluctuations on the outer shells of the ions composing the crystal. In order to discriminate between the charge response in the insulator and the metal suitable models are used being consistent with rigorous sum rules for the density response in the long-wavelength limit of the various phases. In the case of the underdoped phase a response sum rule halfway between that of an insulator and a metal is proposed expressing a loss in the partial density of states for the Cu orbitals at the Fermi level.
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