Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings

TL;DR

This paper implements the full parquet-based dynamical vertex approximation to include all spatial correlations in finite one-dimensional Hubbard models, evaluating its performance against other methods and revealing how non-local correlations influence spectral properties.

Contribution

The paper introduces a full parquet implementation of the dynamical vertex approximation for nanoscopic Hubbard rings, enabling comprehensive analysis of spatial correlations in low-dimensional systems.

Findings

DΓA accurately captures non-local correlations in Hubbard nano-rings.

Comparison shows DΓA's performance relative to DMFT, parquet, and exact solutions.

Non-local correlations significantly modify spectral properties in small systems.

Abstract

We have implemented the dynamical vertex approximation (D$\Gamma$A) in its full parquet-based version to include spatial correlations on all length scales and in {\sl all} scattering channels. The algorithm is applied to study the electronic self-energies and the spectral properties of finite-size one-dimensional Hubbard models with periodic boundary conditions (nanoscopic Hubbard rings). From a methodological point of view, our calculations and their comparison to the results obtained within dynamical mean-field theory, plain parquet approximation, and the exact numerical solution, allow us to evaluate the performance of the D$\Gamma$A algorithm in the most challenging situation of low dimensions. From a physical perspective, our results unveil how non-local correlations affect the spectral properties of nanoscopic systems of various sizes in different regimes of interaction strength.