Truncated Unity Parquet Solver

TL;DR

This paper introduces TUPS, a novel parquet solver using a truncated form-factor basis that efficiently handles large lattice momenta, providing new insights into the Hubbard model and parquet approximation.

Contribution

The paper presents the first implementation of a truncated unity parquet solver with linear scaling, enabling analysis of larger systems and systematic convergence studies.

Findings

TUPS can handle system sizes up to 76x76 momenta.

Single form factor captures qualitative physics of the Hubbard model.

Quantitative accuracy requires multiple form factors at low temperatures.

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 76x76 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 behaviour. Quantitatively, using a single or a few form factors only is not sufficient at lower temperatures or stronger coupling.