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arXiv · 1410.4733

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

A. Valli·T. Schäfer·P. Thunström·G. Rohringer·S. Andergassen·G. Sangiovanni·K. Held·A. Toschi
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Abstract

We have implemented the dynamical vertex approximation (D$Γ$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$Γ$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.

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A. Valli, T. Schäfer, P. Thunström, G. Rohringer, S. Andergassen, G. Sangiovanni, K. Held, A. Toschi. 2015-03-09. Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings. https://doi.org/10.1103/physrevb.91.115115

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