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# The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters

Abstract : We present an embedded-cluster method, based on the TRILEX formalism, that turns the Fierz ambiguity, inherent to approaches based on a bosonic decoupling of local fermionic interactions, into a convergence criterion. It is based on the approximation of the three-leg vertex by a coarse-grained vertex computed by solving a self-consistently determined multi-site effective impurity model. The computed self-energies are, by construction, continuous functions of momentum. We show that, in three interaction and doping regimes of parameters of the two-dimensional Hubbard model, these self-energies are very close to numerically exact benchmark results for clusters of size four only. We show that the Fierz parameter, which parametrizes the freedom in the Hubbard-Stratonovich decoupling, can be used as a quality control parameter. By contrast, the $GW$ +extended dynamical mean field theory approximation with four cluster sites is shown to yield good results only in the weak-coupling regime and for a particular decoupling. Finally, we show that the vertex has spatially nonlocal components only at low energy.
Document type :
Journal articles
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https://hal-cea.archives-ouvertes.fr/cea-01550535
Contributor : Bruno Savelli Connect in order to contact the contributor
Submitted on : Monday, October 3, 2022 - 10:08:58 AM
Last modification on : Wednesday, October 5, 2022 - 3:29:50 AM

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### Citation

Thomas Ayral, Jaksa Vucicevic, Olivier Parcollet. The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters. Physical Review Letters, 2017, 119, pp.166401. ⟨10.1103/PhysRevLett.119.166401⟩. ⟨cea-01550535v2⟩

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