Derivation of the Ghost Gutzwiller Approximation from Quantum Embedding principles: the Ghost Density Matrix Embedding Theory

Abstract

Establishing the underlying links between the diverse landscape of theoretical frameworks for simulating strongly correlated matter is crucial for advancing our understanding of these systems. In this work, we focus on the Ghost Gutzwiller Approximation (gGA), an extension of the Gutzwiller Approximation (GA) based on the variational principle. We derive a framework called "Ghost Density Matrix Embedding Theory" (gDMET) from quantum embedding (QE) principles similar to those in Density Matrix Embedding Theory (DMET), which reproduces the gGA equations for multi-orbital Hubbard models with a simpler implementation. This derivation highlights the crucial role of the ghost degrees of freedom, not only as an extension to the GA, but also as the key element in establishing a consistent conceptual connection between DMET and the gGA. This connection further elucidates how gGA overcomes the systematic accuracy limitations of standard GA and achieves results comparable to Dynamical Mean Field Theory (DMFT). Furthermore, it offers an alternative interpretation of the gGA equations, fostering new ideas and generalizations.

arXiv comment24 pages, 3 figures

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Cited by in corpus (8)

• Accuracy of ghost-rotationally-invariant slave-boson theory for multiorbital Hubbard models and realistic materials
• 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
• Charge self-consistent density functional theory plus ghost rotationally-invariant slave-boson theory for correlated materials
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• A versatile unitary transformation framework for an optimal bath construction in density-matrix based quantum embedding approaches
• Linear Foundation Model for Quantum Embedding: Data-Driven Compression of the Ghost Gutzwiller Variational Space