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The recently introduced coupled cluster (CC) downfolding techniques forreducing the dimensionality of quantum many-body problems recast the CCformalism in the form of the renormalization procedure allowing, for theconstruction of effective (or downfolded) Hamiltonians in small-dimensionalitysub-space, usually identified with the so-called active space, of the entireHilbert 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 determinedas components of the eigenvectors of the downfolded Hamiltonians in the activespace. This paper will discuss the extension of non-Hermitian (associated withstandard CC formulations) and Hermitian (associated with the unitary CCapproaches) downfolding formulations to composite quantum systems. Thenon-Hermitian formulation can provide a platform for developing local CCapproaches, while the Hermitian one can serve as an ideal foundation fordeveloping various quantum computing applications based on the limited quantumresources. We also discuss the algorithm for extracting the semi-analyticalform of the inter-electron interactions in the active spaces.

Coupled Cluster Downfolding Theory: towards efficient many-body algorithms for dimensionality reduction of composite quantum systems