  Single-band Hubbard model at criticality of the metal-insulator transition is
studied using approximations derived from parquet theory. It is argued that
only the electron-hole and interaction two-particle channels in the parquet
algebra are relevant. A scheme is proposed how to reduce the parquet equations
to a manageable form the complexity of which is comparable with single-channel
approximations such as the renormalized RPA. The newly derived approximation,
however, contains dynamical vertex corrections, remains self-consistent at the
two-particle level and allows only for integrable singularities. A
qualitatively new approach for studying two-particle singularities at zero
temperature is obtained.
