Prohibitive cost of accurate quantum many-body methods, like the coupled-cluster method, can be reduced by taking advantage of the sparsity of the wave operator that reveals itself upon some change of representation, such as cluster ("many-body") expansion, localization, rank compression, etc. Although most of the ideas for taking advantage of the sparsity were developed in 1950s to 1980s, efficient realization of these ideas only occured recently. Here we will review the essential developments that led to the modern efficient many-body methods whose cost grows nearly linearly with the system size.

Efficient reduced-scaling many-body electronic structure methods

ACS Fall 2021

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