Derivation of the ghost Gutzwiller approximation from quantum embedding principles: Ghost density matrix embedding theory

Lanatà, Nicola

doi:10.1103/physrevb.108.235112

Phys. Rev. B

2023

DOI: 10.1103/physrevb.108.235112

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Derivation of the ghost Gutzwiller approximation from quantum embedding principles: Ghost density matrix embedding theory

Nicola Lanatà

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Cited by 6 publications

References 69 publications

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A unified density matrix functional construction of quantum baths in density matrix embedding theory beyond the mean-field approximation

Sekaran

Bindech

Fromager

2023

The Journal of Chemical Physics

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The equivalence in one-electron quantum baths between the practical implementation of density matrix embedding theory (DMET) and the more recent Householder-transformed density matrix functional embedding theory has been shown previously in the standard but special case where the reference full-size (one-electron reduced) density matrix, from which the bath is constructed, is idempotent [S. Yalouz et al., J. Chem. Phys. 157, 214112 (2022)]. We prove mathematically that the equivalence remains valid when the density matrix is not idempotent anymore, thus allowing for the construction of correlated (one-electron) quantum baths. A density-matrix functional exactification of DMET is derived within the present unified quantum embedding formalism. Numerical examples reveal that the embedding cluster can be quite sensitive to the level of density-matrix functional approximation used for computing the reference density matrix.

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A unified density matrix functional construction of quantum baths in density matrix embedding theory beyond the mean-field approximation

Sekaran

Bindech

Fromager

2023

The Journal of Chemical Physics

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Fragment quantum embedding using the Householder transformation: A multi-state extension based on ensembles

Cernatic,

Fromager,

Yalouz

2024

The Journal of Chemical Physics

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In recent studies by Yalouz et al. [J. Chem. Phys. 157, 214112 (2022)] and Sekaran et al. [Phys. Rev. B 104, 035121 (2021) and Computation 10, 45 (2022)], density matrix embedding theory (DMET) has been reformulated through the use of the Householder transformation as a novel tool to embed a fragment within extended systems. The transformation was applied to a reference non-interacting one-electron reduced density matrix to construct fragments’ bath orbitals, which are crucial for subsequent ground state calculations. In the present work, we expand upon these previous developments and extend the utilization of the Householder transformation to the description of multiple electronic states, including ground and excited states. Based on an ensemble noninteracting density matrix, we demonstrate the feasibility of achieving exact fragment embedding through successive Householder transformations, resulting in a larger set of bath orbitals. We analytically prove that the number of additional bath orbitals scales directly with the number of fractionally occupied natural orbitals in the reference ensemble density matrix. A connection with the regular DMET bath construction is also made. Then, we illustrate the use of this ensemble embedding tool in single-shot DMET calculations to describe both ground and first excited states in a Hubbard lattice model and an ab initio hydrogen system. Finally, we discuss avenues for enhancing ensemble embedding through self-consistency and explore potential future directions.

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Accuracy of ghost-rotationally-invariant slave-boson theory for multiorbital Hubbard models and realistic materials

Lee,

Melnick,

Adler

et al. 2023

Phys. Rev. B

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Derivation of the ghost Gutzwiller approximation from quantum embedding principles: Ghost density matrix embedding theory

Cited by 6 publications

References 69 publications

A unified density matrix functional construction of quantum baths in density matrix embedding theory beyond the mean-field approximation

A unified density matrix functional construction of quantum baths in density matrix embedding theory beyond the mean-field approximation

Fragment quantum embedding using the Householder transformation: A multi-state extension based on ensembles

Accuracy of ghost-rotationally-invariant slave-boson theory for multiorbital Hubbard models and realistic materials

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