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$Γ$A). Finally, we highlight the potential of AbinitioD$Γ$A by detailing results for the prototypical correlated metal SrVO$_3$.
Electronic correlations and dynamical screening with ab initio quantum embedding
Center for Computational Quantum Physics, Flatiron Institute（Flatiron Institute 计算量子物理中心）；Department of Physics, University of Fribourg（弗里堡大学物理系）；Université Paris-Saclay, CNRS, CEA, Institut de Physique Théorique (IPhT)（巴黎萨克雷大学、法国国家科学研究中心、法国原子能和替代能源委员会、理论物理研究所）；Collège de France（法兰西公学院）；CPHT, CNRS, École Polytechnique, Institut Polytechnique de Paris（巴黎理工学院、法国国立高等矿业电信学校联盟、法国国家科学研究中心计算物理和理论化学中心）；Department of Quantum Matter Physics, University of Geneva（日内瓦大学量子物质物理系）
We characterize experimentally and theoretically the high-energy dielectric screening properties of the prototypical correlated metal SrVO$_3$. The dynamical structure factor measured by inelastic x-ray scattering spectroscopy as a function of momentum transfer is in very good agreement with first-principles calculations in the adiabatic local density approximation to time-dependent density-functional theory. Our results reveal the crucial importance of crystal local fields in the charge response function of correlated materials: They lead to depolarization effects for localised excitations an…
The role of dynamical polarization of the ligand to metal charge transfer excitations in {\em ab initio} determination of effective exchange parameters
Effect of vertex corrections on the longitudinal transport through multilayered nanostructures: Exact dynamical mean-field theory approach applied to the inhomogeneous Falicov-Kimball model
We compute the frequency dependent conductivity of the two dimensional square lattice Hubbard model at zero temperature as a function of density to second order in the interaction strength, and compare the results to the predictions of single-site dynamical mean field theory computed at the same order. We find that despite the neglect of vertex corrections, the single site dynamical mean field approximation produces semiquantitatively accurate results for most carrier concentrations, but fails qualitatively for the nearly empty or nearly filled band cases where the theory exhibits an emergent …
We study the effect of a refined electron-photon vertex on the dynamical breaking of chiral symmetry in reduced quantum electrodynamics. We construct an educated {\em ansatz} for this vertex which satisfies the required discrete symmetries under parity, time reversal and charge conjugation operations. Furthermore, it reproduces its asymptotic perturbative limit in the weak coupling regime and ensures the massless electron propagator is multiplicatively renormalizable in its leading logarithmic expansion. Employing this vertex {\em ansatz}, we solve the gap equation to compute dynamically gener…
In this work, we adapt the formalism of the dynamical vertex approximation (D$Γ$A), a diagrammatic approach including many-body correlations beyond the dynamical mean-field theory, to the case of attractive onsite interactions. We start by exploiting the ladder approximation of the D$Γ$A scheme, in order to derive the corresponding equations for the non-local self-energy and vertex functions of the attractive Hubbard model. Second, we prove the validity of our derivation by showing that the results obtained in the particle-hole symmetric case fully preserve the exact mapping between the attrac…
Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory
In the last decades, dynamical mean-field theory (DMFT) and its diagrammatic extensions have been successfully applied to describe local and nonlocal correlation effects in correlated electron systems. Unfortunately, except for the exact solution, it is impossible to fulfill both the Pauli principle and conservation laws at the same time. Consequently, fundamental observables such as the kinetic and potential energies are ambiguously defined. In this work, we propose an approach to overcome the ambiguity in the calculation of the potential energy within the ladder dynamical vertex approximatio…
We generalize the formalism of the dynamical vertex approximation (D$Γ$A) -- a diagrammatic extension of the dynamical mean-field theory (DMFT)-- to treat magnetically ordered phases. To this aim, we start by concisely illustrating the many-electron formalism for performing ladder resummations of Feynman diagrams in systems with broken SU(2)-symmetry, associated to ferromagnetic (FM) or antiferromagnetic (AF) order. We then analyze the algorithmic simplifications introduced by taking the local approximation of the two-particle irreducible vertex functions in the Bethe-Salpeter equations, which…
Linear response functions from inhomogeneous dynamical mean-field theory
Jožef Stefan Institute（约瑟夫·斯特凡研究所）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学物理学院）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）
We review the electronic structure of nickelate superconductors with and without effects of electronic correlations. As a minimal model we identify the one-band Hubbard model for the Ni 3$d_{x^2-y^2}$ orbital plus a pocket around the $A$-momentum. The latter however merely acts as a decoupled electron reservoir. This reservoir makes a careful translation from {nominal} Sr-doping to the doping of the one-band Hubbard model mandatory. Our dynamical mean-field theory calculations, in part already supported by experiment, indicate that the $Γ$ pocket, Nd 4$f$ orbitals, oxygen 2$p$ and {the} other …
