Browsing by Author "Parcollet, Olivier"

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    Fierz Convergence Criterion: A Controlled Approach to Strongly Interacting Systems with Small Embedded Clusters
    Ayral, Thomas; Vučičević, Jakša; Parcollet, Olivier
    We present an embedded-cluster method, based on the triply irreducible local expansion formalism. It 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 from a self-consistently determined cluster impurity model. The computed self-energies are, by construction, continuous functions of momentum. We show that, in three interaction and doping regimes of the two-dimensional Hubbard model, self-energies obtained with clusters of size four only are very close to numerically exact benchmark results. 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 Matsubara frequencies.
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    Practical consequences of the Luttinger-Ward functional multivaluedness for cluster DMFT methods
    Vučičević, Jakša; Wentzell, Nils; Ferrero, Michel; Parcollet, Olivier
    The Luttinger-Ward functional (LWF) has been a starting point for conserving approximations in many-body physics for 50 years. The recent discoveries of its multivaluedness and the associated divergence of the two-particle irreducible vertex function Γ have revealed an inherent limitation of this approach. Here we demonstrate how these undesirable properties of the LWF can lead to a failure of computational methods based on an approximation of the LWF. We apply the nested cluster scheme (NCS) to the Hubbard model and observe the existence of an additional stationary point of the self-consistent equations, associated with an unphysical branch of the LWF. In the strongly correlated regime, starting with the first divergence of Γ, this unphysical stationary point becomes attractive in the standard iterative technique used to solve DMFT. This leads to an incorrect solution, even in the large cluster size limit, for which we discuss diagnostics.