Unifying Variational and Dynamical Quantum Embedding: From Ghost Gutzwiller Approximation to Dynamical Mean-Field Theory

TL;DR

This paper unifies variational and dynamical quantum embedding methods, demonstrating that ghost-Gutzwiller approximation becomes equivalent to dynamical mean-field theory in the limit of many bath modes, enabling new computational approaches.

Contribution

It proves the formal equivalence between ghost-GA, ghost-DMET, and DMFT, providing a unified framework and finite-temperature extension for studying strongly correlated systems.

Findings

Ghost-GA becomes equivalent to DMFT with infinitely many bath modes.

Provides a finite-temperature extension of ghost-GA.

Allows computation of Green's functions from static expectation values.

Abstract

Dynamical and variational frameworks have long been viewed as distinct paradigms. In particular, in quantum embedding (QE) frameworks, dynamical mean-field theory (DMFT) captures nonperturbative dynamical correlations through a frequency-dependent self-energy, while the Gutzwiller approximation (GA) is formulated in terms of a variationally optimized ground-state wavefunction. Here we bridge these perspectives, proving that the ghost-Gutzwiller approximation (ghost-GA), which also admits a density-matrix-matching QE formulation known as ghost density matrix embedding theory (ghost-DMET), becomes strictly equivalent to DMFT in the limit of infinitely many auxiliary bath modes. This formal unification has immediate consequences. In particular, it yields a rigorous finite-temperature extension of ghost-GA and shows that the physical Green's function can be determined from static expectation values of the embedding Hamiltonians, providing a route to computational studies of competing phases in strongly correlated matter with DMFT-level accuracy, while bypassing the need to calculate dynamical spectra with conventional impurity solvers. More broadly, it shows that the variational ghost-GA, the density-matrix-matching ghost-DMET formulation, and the dynamical DMFT description are not separate constructions, but complementary formulations of the same QE structure, thereby providing a concrete formal basis for future controlled extensions beyond DMFT.