The {\it victory} project v1.0: an efficient parquet equations solver

Abstract

{\it Victory}, i.e. \underline{vi}enna \underline{c}omputational \underline{to}ol deposito\underline{ry}, is a collection of numerical tools for solving the parquet equations for the Hubbard model and similar many body problems. The parquet formalism is a self-consistent theory at both the single- and two-particle levels, and can thus describe individual fermions as well as their collective behavior on equal footing. This is essential for the understanding of various emergent phases and their transitions in many-body systems, in particular for cases in which a single-particle description fails. Our implementation of {\it victory} is in modern Fortran and it fully respects the structure of various vertex functions in both momentum and Matsubara frequency space. We found the latter to be crucial for the convergence of the parquet equations, as well as for the correct determination of various physical observables. In this release, we thoroughly explain the program structure and the controlled approximations to efficiently solve the parquet equations, i.e. the two-level kernel approximation and the high-frequency regulation.

arXiv commentThe first release of victory code; 14 pages, 9 figures

References in corpus (4)

• Functional renormalization group approach to correlated fermion systems
• Local Electronic Correlation at the Two-Particle Level
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• Efficient implementation of the parquet equations -- role of the reducible vertex function and its kernel approximation

Cited by in corpus (4)

• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Analytical investigation of singularities in two-particle irreducible vertex functions of the Hubbard atom
• Dual parquet scheme for the two-dimensional Hubbard model: modelling low-energy physics of high-$T_c$ cuprates with high momentum resolution
• Truncated-Unity Parquet Equations: Application to the Repulsive Hubbard Model