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

Abstract

In this work, we introduce an original self-consistent scheme based on the one-body reduced density matrix ($\gamma$) formalism. A significant feature of this methodology is the utilization of an optimal unitary transformation of the Hamiltonian, determined through a self-consistently determined, unitary reflection $\mathbf{R}[\gamma ]$. This enables the extraction of all reduced properties 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 local virial-like relation, providing quantitative insight into the correspondence between the fragment in the extended system and its embedded analogue. The performance and convergence of the method, as well as the N-representability of the resulting correlated density matrix, are evaluated and discussed within the context of the one-dimensional Hubbard model, which provides exact results for a comprehensive comparison.

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• Quantum embedding theories
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• Fragment quantum embedding using the Householder transformation: a multi-state extension based on ensembles
• Local Potential Functional Embedding Theory of Molecular Systems: Localized Orbital-Based Embedding from an Exact Density-Functional Perspective
• A versatile unitary transformation framework for an optimal bath construction in density-matrix based quantum embedding approaches
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions