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In this work, we introduce an original self-consistent scheme based on theone-body reduced density matrix ($\gamma$) formalism. A significant feature ofthis methodology is the utilization of an optimal unitary transformation of theHamiltonian, determined through a self-consistently determined, unitaryreflection $\mathbf{R}[\gamma]$. This enables the extraction of all reducedproperties of the system from a smaller, accurately solved embedding cluster,and to systematically reconstruct the reduced density matrix of the system.This process ensures that both extended and embedded systems satisfy the localvirial-like relation, providing quantitative insight into the correspondencebetween the fragment in the extended system and its embedded analogue. Theperformance and convergence of the method, as well as the N-representability ofthe resulting correlated density matrix, are evaluated and discussed within thecontext of the one-dimensional Hubbard model, which provides exact results fora comprehensive comparison.

physical review. b./physical review. b

Unitary transformations within density matrix embedding approaches: A  novel perspective on the self-consistent scheme for electronic structure  calculation