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 ${\mathrm{H}}_5$.

中文翻译：

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多粒子波函数的精确两体展开

波函数的指数复杂性阻碍了解决强相关电子问题的进展。先前的工作为基态波函数建立了精确的两体指数积展开。通过开发Dalgarno-Lewis扰动理论的密度矩阵简化的模型，我们在这里证明（i）两体指数乘积展开迅速且全局收敛，每个算子代表重新归一化扰动理论的阶数；（ii）扩展的能量在解附近二次方收敛，并且（iii）扩展对于基态和激发态都是精确的。两体扩展提供了减少的多粒子波函数的参数化以及两粒子密度降低的矩阵，在常规计算机和量子计算机上都有潜在的应用，可用于研究强相关的量子系统。我们用分子链的紧缩Schrödinger方程的精确解证明了结果${\mathrm{H}}_4$ 和 ${\mathrm{H}}_5$。