Dual-space cluster-diagrammatic approach to nonlocal electronic correlations

TL;DR

This paper introduces a cluster extension of the D-TRILEX approach to better capture nonlocal electronic correlations, demonstrating improved accuracy over existing methods in a one-dimensional Hubbard model.

Contribution

The authors develop a cluster-based D-TRILEX method that combines short-range exact treatment with long-range fluctuation descriptions, reducing periodization ambiguity and improving accuracy.

Findings

Accurately reproduces the electronic self-energy at Fermi momenta.

Outperforms parquet dynamical vertex approximation in accuracy.

Reduces periodization ambiguity compared to CDMFT.

Abstract

In this work, we extend the dual triply irreducible local expansion (D-TRILEX) approach for correlated electronic systems by introducing a cluster reference system for the diagrammatic expansion. This framework allows us to consistently combine the exact treatment of short-range correlation effects within the cluster, with an efficient diagrammatic description of the long-range charge and spin collective fluctuations beyond the cluster. We demonstrate the effectiveness of our approach by applying it to the one-dimensional nano-ring Hubbard model, where the low dimensionality enhances non-local correlations. Our results show that the cluster extension of D-TRILEX accurately reproduces the electronic self-energy at momenta corresponding to the Fermi energy, in good agreement with the reliable Hirsch-Fye quantum Monte Carlo solution of the problem. We further compare this method with the more computationally demanding parquet dynamical vertex approximation and find that, our method yields substantially more accurate results at momenta associated with the Fermi surface. We show that the D-TRILEX diagrammatic extension drastically reduces the periodization ambiguity of cluster quantities when mapping back to the original lattice, compared to cluster dynamical mean-field theory (CDMFT). Furthermore, we identify the CDMFT impurity problem as the main source of the translational-symmetry breaking and propose a computational scheme for improving the starting point for the cluster-diagrammatic expansion.