Exact Two-body Expansion of the Many-particle Wave Function

TL;DR

This paper introduces an exact two-body exponential product expansion for many-particle wave functions, demonstrating rapid convergence and applicability to strongly correlated systems, including molecular chains, with potential use in quantum computing.

Contribution

It proves the convergence and exactness of the two-body exponential product expansion for ground and excited states, advancing wave function parametrization methods.

Findings

The expansion converges rapidly and quadratically near the solution.

It is exact for both ground and excited states.

Demonstrated with molecular chains H4 and H5.

Abstract

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$_{5}$.