Momentum-Space Cluster Dual Fermion Method

Abstract

Recent years have seen the development of two types of non-local extensions to the single-site dynamical mean field theory. On one hand, cluster approximations, such as the dynamical cluster approximation, recover short-range momentum-dependent correlations non-perturbatively. On the other hand, diagrammatic extensions, such as the dual fermion theory, recover long ranged corrections perturbatively. The correct treatment of both strong short-ranged and weak long-ranged correlations within the same framework is therefore expected to lead to a quick convergence of results, and offers the potential of obtaining smooth self-energies in non-perturbative regimes of phase space. In this paper, we present an exact cluster dual fermion method based on an expansion around the dynamical cluster approximation. Unlike previous formulations, our method does not employ a coarse graining approximation to the interaction, which we show to be the leading source of error at high temperature, and converges to the exact result independent of the size of the underlying cluster. We illustrate the power of the method with results for the second-order cluster dual fermion approximation to the single-particle self-energies and double occupancies.

12 pages, 5 figures

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• Algorithmic Matsubara Integration for Hubbard-like models
• Dual Boson Diagrammatic Monte Carlo Approach Applied to the Extended Hubbard Model
• Local Plaquette Physics as Key Ingredient of High-Temperature Superconductivity in Cuprates
• Second-order dual fermion approach to the Mott transition in the two-dimensional Hubbard model
• Compactness of quantics tensor train representations of local imaginary-time propagators
• Second-order dual fermion for multi-orbital systems
• The finite-difference parquet method: Enhanced electron-paramagnon scattering opens a pseudogap
• Dual-space cluster-diagrammatic approach to nonlocal electronic correlations