Practical consequences of the Luttinger-Ward functional multivaluedness for cluster DMFT methods

2017/09/30 by J. Vučičević, Jaksa Vucicevic, Nils Wentzell +2 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Cluster (spacecraft) #Combinatorics #Computer science #Divergence (linguistics) #Function (biology) #Hubbard model #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Point (geometry) #Quantum and electron transport phenomena #Quantum mechanics #Statistical physics #Superconductivity #Theoretical physics #Vertex (graph theory) #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.97.125141

published as Phys. Rev. B 97, 125141 (2018) · 28 pages, 22 figures, v3 PRB structure, and minor corrections

openalex created_date 2017/10/06 · arxiv created 2018/02/07 · openalex publication_date 2018/03/23 · arxiv updated 2018/03/28 · openalex updated_date 2026/08/05

Abstract

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 \mathrm\ensuremathΓ 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 \mathrm\ensuremathΓ, 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.

Citations

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