2015/10/12 by Gang Li, Nils Wentzell, Petra Pudleiner +2 · 2 citations
Mathematics · Physics and Astronomy · #Discrete mathematics #Formalism (music) #Kernel (algebra) #Mathematical analysis #Mathematical physics #Mathematics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum and electron transport phenomena #Vertex (graph theory) #Vertex function #Vertex model #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.93.165103
published as Phys. Rev. B 93, 165103 (2016) · 12 pages, 11 figures
arxiv created 2015/10/12 · openalex publication_date 2016/04/04 · arxiv updated 2016/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We present an efficient implementation of the parquet formalism that respects the asymptotic structure of the vertex functions at both single- and two-particle levels in momentum and frequency space. We identify the two-particle reducible vertex as the core function that is essential for the construction of the other vertex functions. This observation stimulates us to consider a two-level parameter reduction for this function to simplify the solution of the parquet equations. The resulting functions, which depend on fewer arguments, are coined ``kernel functions.'' With the use of the kernel functions, the open boundary of various vertex functions in Matsubara-frequency space can be faithfully satisfied. We justify our implementation by accurately reproducing the dynamical mean-field theory results from momentum-independent parquet calculations. The high-frequency asymptotics of the single-particle self-energy and the two-particle vertex are correctly reproduced, which turns out to be essential for the self-consistent determination of the parquet solutions. The current implementation is also feasible for the dynamical vertex approximation.