  Progress toward the solution of the strongly correlated electron problem has
been stymied by the exponential complexity of the wave function. Previous work
established an exact two-body exponential product expansion for the
ground-state wave function. By developing a reduced density matrix analogue of
Dalgarno-Lewis perturbation theory, we prove here that (i) the two-body
exponential product expansion is rapidly and globally convergent with each
operator representing an order of a renormalized perturbation theory, (ii) the
energy of the expansion converges quadratically near the solution, and (iii)
the expansion is exact for both ground and excited states. The two-body
expansion offers a reduced parametrization of the many-particle wave function
as well as the two-particle reduced density matrix with potential applications
on both conventional and quantum computers for the study of strongly correlated
quantum systems. We demonstrate the result with the exact solution of the
contracted Schr\"odinger equation for the molecular chains H$_{4}$ and H$_{5}$.
