Spin fluctuations and covalence in the half-filled narrow-band Hubbard model

We calculate the spin density within the widely accepted model for the insulating parents (${\mathrm{La}}_2$${\mathrm{CuO}}_4$ and ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_6$) of the superconducting cuprates, namely, the half-filled narrow-one-band Hubbard model as mapped from the three-band model for the ${\mathrm{CuO}}_2$ planes. The result, which includes quantum spin fluctuations and covalence simultaneously, disagrees strongly with neutron-diffraction results. Possible remedies are discussed. A reinterpretation of the neutron data on the high-temperature-superconducting parents gives considerable, but insufficient, improvement.