Related papers: Green's Functions for the Anderson model: the Atom…
We study various asymptotic approximations of Good's special functions arising in atomic physics. These special functions are situated beyond Anger's functions to which they are closely related. Our major tool is the method of the…
The cumulant expansion of the Green's function is a computationally efficient beyond-$GW$ approach renowned for its significant enhancement of satellite features in materials. In contrast to the ubiquitous $GW$ approximation of many-body…
We combine the recently developed many-body Green's function theory for electrons and nuclei with the exact factorization of the wave function. The existing Born-Oppenheimer Green's functions are shown to be special cases of our exact…
The Anderson impurity model for Kondo problem is investigated for arbitrary orbit-spin degeneracy $N$ of the magnetic impurity by the equation of motion method (EOM). By employing a new decoupling scheme, a set self-consistent equations for…
We develop a method for calculating the self-energy of a quantum impurity coupled to a continuous bath by stochastically generating a distribution of finite Anderson models that are solved by exact diagonalization, using the noninteracting…
Ground-state properties of the non-interacting symmetric single-impurity Anderson model (SIAM) are derived from the corresponding eigenenergy equation. Explicit formulae are given for the ground-state energy, the hybridization, and the…
The uniform asymptotic approximation method provides a powerful, systematically-improved, and error-controlled approach to construct accurate analytical approximate solutions of mode functions of perturbations of the…
Based on the Green's function (GF) equation-of-motion formalism, we develop a method to expand the double time Green's function into Taylor series of the parameter $\lambda$ in the Hamiltonian $H=H_0 + \lambda H_1$. Here $H_0$ is the…
The self-energy method for quantum impurity models expresses the correlation part of the self-energy in terms of the ratio of two Green's functions and allows for a more accurate calculation of equilibrium spectral functions than is…
We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the…
We present a new, highly efficient yet accurate approximation for the Green's functions of dressed particles, using the Holstein polaron as an example. Instead of summing a subclass of diagrams (e.g. the non-crossed ones, in the…
Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions (P. Fan et al., Phys. Rev. B 97, 165140 (2018)). In that approximation, the precision of results depends on the…
Pad\'e approximants to the many-body Green's function can be built by rearranging terms of its perturbative expansion. The hypothesis that the best use of a finite number of terms of such an expansion is given by the subclass of diagonal…
Gaussian process (GP) emulator has been used as a surrogate model for predicting force field and molecular potential, to overcome the computational bottleneck of molecular dynamics simulation. Integrating both atomic force and energy in…
We review two analytical approaches in Dynamical Mean-Field Theory (DMFT) based on a perturbation theory expansion over the electron hopping to and from the self consistent environment. In the first approach the effective single impurity…
In a typical scenario the diagrammatic many-body perturbation theory generates asymptotic series. Despite non-convergence, the asymptotic expansions are useful when truncated to a finite number of terms. This is the reason for popularity of…
We introduce an improved approach for obtaining smooth finite-temperature spectral functions of quantum impurity models using the numerical renormalization group (NRG) technique. It is based on calculating first the Green's function on the…
Previously, we introduced a method for systematically correcting a quasiparticle green's function via a power series expansion. Here we present an ODE based formalisms of power series correction that goes beyond the cumulant approximation…
Basing on the relation between the Coulomb Green function and the Green function of harmonic oscillator, the algebraic representation of the many-particle Coulomb Green function in the form of annihilation and creation operators is…
The Sturmian expansion of the generalized Dirac--Coulomb Green function [R.\/~Szmytkowski, J.\ Phys.\ B \textbf{30}, 825 (1997); \textbf{30}, 2747(E) (1997)] is exploited to derive a closed-form expression for the magnetizability of the…