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

• Published in: arXiv.org
• Main Authors: Valli, A, Schäfer, T, Thunström, P, Rohringer, G, Andergassen, S, Sangiovanni, G, Held, K, Toschi, A
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 09.03.2015
• Subjects: Algorithms; Approximation; Boundary conditions; Mathematical analysis; Mathematical models; Mean field theory; Physics - Strongly Correlated Electrons
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1410.4733

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.