Related papers: Analytic continuation with Pad\'e decomposition
In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…
We derive equations of motion for Green's functions of the multi-orbital Anderson impurity model by differentiating symmetrically with respect to all time arguments. The resulting equations relate the one- and two-particle Green's function…
We present a spectral weight conserving formalism for Fermionic thermal Green's functions that are discretized in imaginary time and thus periodic in imaginary ("Matsubara") frequency. The formalism requires a generalization of the Dyson…
By merging algorithmic Matsubara integration with discrete pole representations we present a procedure to generate fully analytic closed form results for impurity problems at fixed perturbation order. To demonstrate the utility of this…
We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…
Flexible boundary condition methods couple an isolated defect to bulk through the bulk lattice Green's function. The inversion of the force-constant matrix for the lattice Green's function requires Fourier techniques to project out the…
Including finite-temperature effects from the electronic degrees of freedom in electronic structure calculations of semiconductors and metals is desired; however, in practice it remains exceedingly difficult when using zero-temperature…
We consider a general class of approximations which guarantees the conservation of particle number in many-body perturbation theory. To do this we extend the concept of $\Phi$-derivability for the self-energy $\Sigma$ to a larger class of…
In the graph-based semi-supervised learning, the Green-function method is a classical method that works by computing the Green's function in the graph space. However, when applied to large graphs, especially those sparse ones, this method…
Analytic continuation (AC) from imaginary-time Green's function to spectral function is essential in the numerical analysis of dynamical properties in quantum many-body systems. However, this process faces a fundamental challenge: it is an…
Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations…
We present a data-driven approach to mathematically model physical systems whose governing partial differential equations are unknown, by learning their associated Green's function. The subject systems are observed by collecting…
A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…
Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space described by the matrix-valued Herglotz-Nevanlinna structure can…
Functional renormalization group equations are analytically continued from imaginary Matsubara frequencies to the real frequency axis. On the example of a scalar field with O(N) symmetry we discuss the analytic structure of the flowing…
In this work, we use rational approximation to improve the accuracy of spectral solutions of differential equations. When working in the vicinity of solutions with singularities, spectral methods may fail their propagated spectral rate of…
This paper, Part I in a two-part series, presents (i) A simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well as (ii) An associated boundary-integral equation method for the numerical solution of…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
Radiative corrections to an atom are calculated near a half-space that has arbitrarily-shaped small depositions upon its surface. The method is based on calculation of the classical Green's function of the macroscopic Maxwell equations near…
In this article we obtain new irrationality measures for values of functions which belong to a certain class of hypergeometric functions including shifted logarithmic functions, binomial functions and shifted exponential functions. We…