Exact two-body expansion of the many-particle wave function

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 analog 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 Schrödinger equation for the molecular chains ${\mathrm{H}}_4$ and ${\mathrm{H}}_5$.

Figure 1

The potential energy curves of ${\mathrm{H}}_4$ from Hartree-Fock (HF), MP2, CCSD(T), CSE(2), and FCI are shown. The CSE(2) energies, shown by solid circles (red), are in exact agreement with the black line of FCI.