Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

Abstract

Strong electronic correlations pose one of the biggest challenges to solid state theory. We review recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT). On top of this, non-local correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge-, magnetic-, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. We provide an overview of the successes and results achieved---hitherto mainly for model Hamiltonians---and outline future prospects for realistic material calculations.

60 pages, 42 figures, replaced by the version to be published in Rev. Mod. Phys. 2018

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• Antiferromagnetic magnons and local anisotropy: dynamical mean-field study
• Efficient slave-boson approach for multiorbital two-particle response functions and superconductivity
• Nonpertubative Many-Body Theory for the Two-Dimensional Hubbard Model at Low Temperature: From Weak to Strong Coupling Regimes
• Functional renormalization with interaction flows: A single-boson exchange perspective and application to electron-phonon systems
• Variational Diagrammatic Monte-Carlo Built on Dynamical Mean-Field Theory
• Strong-coupling formula for momentum-dependent susceptibilities in dynamical mean-field theory
• Surfaces and interfaces of infinite-layer nickelates studied by dynamical mean-field theory
• Quantitative Description of Strongly Correlated Materials by Combining Downfolding Techniques and Tensor Networks
• Improvement of the simplification method for the local two-particle full-vertex towards precise frequency behavior
• Long-term memory magnetic correlations in the Hubbard model: A dynamical mean-field theory analysis
• Multi-band D-TRILEX approach to materials with strong electronic correlations
• Eliminating Orbital Selectivity from the Metal-Insulator Transition by Strong Magnetic Fluctuations
• Fluctuating local field method for the disordered Ising model
• Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model
• The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model