On the duality of ring and ladder diagrams and its importance for many-electron perturbation theories

Abstract

We present a diagrammatic decomposition of the transition pair correlation function for the uniform electron gas. We demonstrate explicitly that ring and ladder diagrams are dual counterparts that capture significant long- and short-ranged interelectronic correlation effects, respectively. Our findings help to guide the further development of approximate many-electron theories and reveal that the contribution of the ladder diagrams to the electronic correlation energy can be approximated in an effective manner using second-order perturbation theory. We employ the latter approximation to reduce the computational cost of coupled cluster theory calculations for insulators and semiconductors by two orders of magnitude without compromising accuracy.

arXiv comment6 pages, 2 figures, 1 table

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• Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems
• Effective Hamiltonians for the study of real metals using quantum chemical theories
• Averting the infrared catastrophe in the gold standard of quantum chemistry
• A basis-set error correction based on density-functional theory for strongly correlated molecular systems
• Surface science using coupled cluster theory via local Wannier functions and in-RPA-embedding: the case of water on graphitic carbon nitride
• A comparative study using state-of-the-art electronic structure theories on solid hydrogen phases under high pressures
• Towards Pair Atomic Density Fitting for Correlation Energies with Benchmark Accuracy
• Focal-point approach with pair-specific cusp correction for coupled-cluster theory
• Assessment of the second-order statically screened exchange correction to the random phase approximation for correlation energies
• Dynamical correlation energy of metals in large basis sets from downfolding and composite approaches
• Accelerating the Convergence of Auxiliary-Field Quantum Monte Carlo inSolids with Optimized Gaussian Basis Sets
• Accelerating convergence to the thermodynamic limit with twist angle selection applied to methods beyond many-body perturbation theory
• Ground-States for Metals from Converged Coupled Cluster Calculations