Efficient implementation of the parquet equations: Role of the reducible vertex function and its kernel approximation

Gang Li, Nils Wentzell, Petra Pudleiner, Patrik Thunström, and Karsten Held
Phys. Rev. B 93, 165103 – Published 4 April 2016

Abstract

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.

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  • Received 18 October 2015
  • Revised 11 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.165103

©2016 American Physical Society

Authors & Affiliations

Gang Li1,*, Nils Wentzell1,2, Petra Pudleiner1, Patrik Thunström1, and Karsten Held1

  • 1Institute of Solid State Physics, Vienna University of Technology, A-1040 Vienna, Austria
  • 2Institut für Theoretische Physik and CQ Center for Collective Quantum Phenomena, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany

  • *Author to whom all correspondence should be addressed: gangli.phy@gmail.com

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Vol. 93, Iss. 16 — 15 April 2016

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