Truncated unity parquet solver

Physical review. B./Physical review. B, vol. 101

Abstract

We present an implementation of a truncated unity parquet solver (TUPS) which solves the parquet equations using a truncated form-factor basis for the fermionic momenta. This way fluctuations from different scattering channels are treated on an equal footing. The essentially linear scaling of computational costs in the number of untruncated bosonic momenta allows us to treat system sizes of up to $76\ifmmode\times\else\texttimes\fi{}76$ discrete lattice momenta, unprecedented by previous unbiased methods that include the frequency dependence of the vertex. With TUPS, we provide the first numerical evidence that the parquet approximation might indeed respect the Mermin-Wagner theorem and further systematically analyze the convergence with respect to the number of form factors. Using a single form factor seems to qualitatively describe the physics of the half-filled Hubbard model correctly, including the pseudogap behavior. Quantitatively, using a single or a few form factors only is not sufficient at lower temperatures or stronger coupling.

Authors 4

1. Christian Eckhardt Aachen Institute for Theoretical Solid State Physics

   TU Wien · RWTH Aachen University

   Affiliation as printed

   Institute for Solid State Physics, TU Wien, 1040 Vienna, Austria

   Institute for Theoretical Solid State Physics, RWTH Aachen University, 52074 Aachen, Germany

2. Carsten Honerkamp Aachen Institute for Theoretical Solid State Physics

   Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   Institute for Theoretical Solid State Physics, RWTH Aachen University, 52074 Aachen, Germany

   JARA-FIT, Jülich Aachen Research Alliance - Fundamentals of Future Information Technology, 52425 Jülich, Germany

3. Karsten Held

   TU Wien

   Affiliation as printed

   Institute for Solid State Physics, TU Wien, 1040 Vienna, Austria

4. Anna Kauch

   TU Wien

   Affiliation as printed

   Institute for Solid State Physics, TU Wien, 1040 Vienna, Austria