The victory project v1.0: An efficient parquet equations solver

Published: 23-04-2019| Version 1 | DOI: 10.17632/ym5kscj9sz.1
Gang Li,
Anna Kauch,
Petra Pudleiner,
Karsten Held


Victory, i.e. vienna computational tool depository, is a collection of numerical tools for solving the parquet equations for the Hubbard model and similar many body problems. In the current release, we focus on the single-band 2D Hubbard model, based on which generalizations to non-local interactions, multi orbitals and other lattices are straightforward. 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 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.