耦合团簇下折叠理论：复合量子系统降维的高效多体算法
Coupled Cluster Downfolding Theory: towards efficient many-body algorithms for dimensionality reduction of composite quantum systems
摘要：
最近引入的耦合团簇（CC）下折叠技术，用于减少量子多体问题的维数重铸的CC形式主义的重整化过程的形式，允许，为有效的（或下折叠的）哈密尔顿在小维子空间的建设，通常与所谓的活动空间，整个希尔伯特空间。所得到的下折哈密顿量从波函数的内部（在活动空间内）参数中积分出外部（活动空间外）费米自由度，所述内部参数可以被确定为活动空间中的下折哈密顿量的本征向量的分量。本文将讨论扩展的非厄米特（与标准CC配方）和厄米特（与酉CC方法）向下折叠配方复合量子系统。非厄米特公式可以为发展局域CC方法提供平台，而厄米特公式可以作为基于有限量子资源开发各种量子计算应用的理想基础。我们还讨论了提取活性空间中电子间相互作用的半解析形式的算法。
英文摘要：
The recently introduced coupled cluster (CC) downfolding techniques for reducing the dimensionality of quantum many-body problems recast the CC formalism in the form of the renormalization procedure allowing, for the construction of effective (or downfolded) Hamiltonians in small-dimensionality sub-space, usually identified with the so-called active space, of the entire Hilbert space. The resulting downfolded Hamiltonians integrate out the external (out-of-active-space) Fermionic degrees of freedom from the internal (in-the-active-space) parameters of the wave function, which can be determined as components of the eigenvectors of the downfolded Hamiltonians in the active space. This paper will discuss the extension of non-Hermitian (associated with standard CC formulations) and Hermitian (associated with the unitary CC approaches) downfolding formulations to composite quantum systems. The non-Hermitian formulation can provide a platform for developing local CC approaches, while the Hermitian one can serve as an ideal foundation for developing various quantum computing applications based on the limited quantum resources. We also discuss the algorithm for extracting the semi-analytical form of the inter-electron interactions in the active spaces.
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