Effective interactions in multi-band systems from constrained summations

Abstract

In correlated electron materials, the application of many-body techniques for the study of interaction effects or unconventional superconductivity often requires the formulation of an effective low-energy model that contains only the relevant bands near the Fermi level. However the bands away from the Fermi level are known to renormalize the low-energy interactions substantially. Here we compare different schemes to derive low-energy effective theories for interacting electrons in solids. The frequently used constrained random phase approximation (cRPA) is identified as a particular resummation of higher-order interaction terms that includes important virtual corrections. We then propose an adapted functional renormalization group (fRG) scheme that includes the cPRA, but also allows one to go beyond the cRPA approximation. We study a simple two-band model in order to explore the differences between the approximations.

18 pages, 11 figures

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Cited by in corpus (17)

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• Accuracy of downfolding based on the constrained random phase approximation
• Random Phase Approximation for gapped systems: role of vertex corrections and applicability of the constrained random phase approximation
• Downfolding from Ab Initio to Interacting Model Hamiltonians: Comprehensive Analysis and Benchmarking of the DFT+cRPA Approach
• Efficient vertex parametrization for the constrained functional renormalization group for effective low-energy interactions in multiband systems
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• Investigation of the effective interactions for the Emery model by the constrained random-phase approximation and constrained functional renormalization group
• Model-mapped random phase approximation to evaluate superconductivity in the fluctuation exchange approximation from first principles
• Functional renormalization and mean-field approach to multiband systems with spin-orbit coupling: Application to the Rashba model with attractive interaction
• Static treatment of dynamic interactions in the single-orbital Anderson impurity model
• A functional renormalization group approach to electronic structure calculations for systems without translational symmetry
• Kekulé order from diffuse nesting near higher-order Van Hove points
• Theory of unconventional magnetism in a Cu-based kagome metal