Towards ab initio calculations with the dynamical vertex approximation

Abstract

While key effects of the many-body problem---such as Kondo and Mott physics---can be understood in terms of on-site correlations, non-local fluctuations of charge, spin, and pairing amplitudes are at the heart of the most fascinating and unresolved phenomena in condensed matter physics. Here, we review recent progress in diagrammatic extensions to dynamical mean-field theory for ab initio materials calculations. We first recapitulate the quantum field theoretical background behind the two-particle vertex. Next we discuss latest algorithmic advances in quantum Monte Carlo simulations for calculating such two-particle quantities using worm sampling and vertex asymptotics, before giving an introduction to the ab initio dynamical vertex approximation (AbinitioD$\Gamma$A). Finally, we highlight the potential of AbinitioD$\Gamma$A by detailing results for the prototypical correlated metal SrVO${}_3$.

8 pages, 8 figures; JPSJ Special Topics "New ab inito approaches to explore emergent phenomena in quantum matters"

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Cited by in corpus (19)

• Thermoelectricity in correlated narrow-gap semiconductors
• Impact of partially bosonized collective fluctuations on electronic degrees of freedom
• Self-consistent ladder D$\Gamma$A approach
• The AbinitioD$\Gamma$A Project v1.0: Non-local correlations beyond and susceptibilities within dynamical mean-field theory
• Local and nonlocal electronic correlations at the metal-insulator transition in the Hubbard model in two dimensions
• Hall and Faraday effects in interacting multi-band systems with arbitrary band topology and spin-orbit coupling
• Extended regime of coexisting metallic and insulating phases in a two-orbital electronic system
• Charge Density Wave Ordering in NdNiO${}_2$: Effects of Multiorbital Nonlocal Correlations
• Improved effective vertices in the multi-orbital Two-Particle Self-Consistent method from Dynamical Mean-Field Theory
• Multi-channel fluctuating field approach to competing instabilities in interacting electronic systems
• Dual Bethe-Salpeter equation for the multi-orbital lattice susceptibility within dynamical mean-field theory
• Self-energy self-consistent density functional theory plus dynamical mean field theory
• Splitting of electronic spectrum in paramagnetic phase of itinerant ferromagnets and altermagnets
• Simplification of the local full vertex in the impurity problem in DMFT and its applications for the nonlocal correlation
• Orbital isotropy of magnetic fluctuations in correlated electron materials induced by Hund's exchange coupling
• Exchange interactions in itinerant magnets: the effects of local particle-hole irreducible vertex corrections and SU(2) symmetry of Hund interaction
• Dual-space cluster-diagrammatic approach to nonlocal electronic correlations
• Strong-coupling formula for momentum-dependent susceptibilities in dynamical mean-field theory
• Multi-band D-TRILEX approach to materials with strong electronic correlations