# 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.
Type de document :
Pré-publication, Document de travail
t17/104. 14 pages. 2017
Domaine :

Littérature citée [69 références]

https://hal-cea.archives-ouvertes.fr/cea-01550535
Contributeur : Emmanuelle De Laborderie <>
Soumis le : jeudi 29 juin 2017 - 15:59:07
Dernière modification le : vendredi 27 avril 2018 - 19:26:01
Document(s) archivé(s) le : jeudi 18 janvier 2018 - 02:26:19

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1706.01388.pdf
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• HAL Id : cea-01550535, version 1
• ARXIV : 1706.01388

### Citation

Thomas Ayral, Jaksa Vucicevic, Olivier Parcollet. The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters. t17/104. 14 pages. 2017. 〈cea-01550535〉

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