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

Thomas Ayral (1, 2) , Jaksa Vucicevic (3, 2) , Olivier Parcollet (2)

1 Department of Physics and Astronomy [Piscataway]
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681
3 Institute of Physics [Belgrade]

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.

Domaines: Physique [physics]; Electrons fortement corrélés [cond-mat.str-el]

Thomas Ayral, Jaksa Vucicevic, Olivier Parcollet. The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters. 2017. ⟨cea-01550535v1⟩