The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model

TL;DR

This paper introduces a bosonization-based numerical method for the parquet approximation in the 2D Hubbard model, enabling analysis of larger lattices with full momentum and frequency resolution, advancing computational capabilities.

Contribution

It presents a novel bosonization approach to the parquet approximation, improving computational efficiency and allowing larger lattice studies in the 2D Hubbard model.

Findings

Successfully applied to a 16x16 lattice at weak coupling.

Retained full momentum and frequency structure of vertex functions.

Discussed symmetries and parametrizations of vertex functions.

Abstract

The parquet approach to vertex corrections is unbiased but computationally demanding. Most applications are therefore restricted to small cluster sizes or rely on various simplifying approximations. We have recently shown that the bosonization of the parquet diagrams provides interpretative and algorithmic advantages over the original purely fermionic formulation. Here we present first results of the numerical implementation of this method by applying it to the half-filled Hubbard model on the square lattice at weak coupling. The improved algorithmic performance allows us to evaluate the parquet approximation for a $16\times16$ lattice, retaining the full momentum and frequency structure of the various vertex functions. We discuss their symmetries and consider parametrizations of their momentum dependence using the truncated unity approximation.