Parquet approximation for the 4x4 Hubbard cluster

TL;DR

This paper introduces a numerical solution for the parquet approximation applied to a 4x4 Hubbard cluster, showing it aligns well with quantum Monte Carlo results and outperforms other approximation methods.

Contribution

The paper develops and applies a self-consistent parquet approximation with a simplified irreducible vertex to the Hubbard model on a 4x4 cluster, demonstrating its effectiveness.

Findings

Good agreement with DQMC results

Outperforms FLEX and second-order approximations

Provides a self-consistent diagrammatic approach

Abstract

We present a numerical solution of the parquet approximation (PA), a conserving diagrammatic approach which is self-consistent at both the single-particle and the two-particle levels. The fully irreducible vertex is approximated by the bare interaction thus producing the simplest approximation that one can perform with the set of equations involved in the formalism. The method is applied to the Hubbard model on a half-filled 4x4 cluster. Results are compared to those obtained from Determinant Quantum Monte Carlo (DQMC), FLuctuation EXchange (FLEX), and self-consistent second-order approximation methods. This comparison shows a satisfactory agreement with DQMC and a significant improvement over the FLEX or the self-consistent second-order approximation.