Related papers: Controllable Precision of the Projective Truncatio…
In the equation of motion approach to the two-time Green's functions, conventional Tyablikov-type truncation of the chain of equations is rather arbitrary and apt to violate the analytical structure of Green's functions. Here, we propose a…
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 introduce a general scheme to consistently truncate equations of motion for Green's functions. Our scheme is guaranteed to generate physical Green's functions with real excitation energies and positive spectral weights. There are free…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
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…
A method based on separated integration to estimate anharmonic corrections to energy and vibration of molecules in a second-order diagrammatic vibrational many-body Green's function formalism has already been presented. A severe bottleneck…
We propose an improved quantum algorithm to calculate the Green's function through real-time propagation, and use it to compute the retarded Green's function for the 2-, 3- and 4-site Hubbard models. This novel protocol significantly…
Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…
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…
A modified $GW$ approximation to many - body systems is developed. The approximation has the same computational complexity as the traditional $GW$ approach, but uses a different truncation scheme. This scheme neglects high order connected…
Machine learning methods are applied to finding the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Different methods of parametrizing the Green's function are…
The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between…
We consider the cumulant expansion of the PAM employing the hybridization as perturbation (Phys. Rev. B 50, 17933 (1994)), and we obtain formally exact one-electron Green's functions (GF). These GF contain effective cumulants that are as…
Computation of the Green's function is crucial to study the properties of quantum many-body systems such as strongly correlated systems. Although the high-precision calculation of the Green's function is a notoriously challenging task on…
We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians…
We present an impurity solver based on adaptively truncated Hilbert spaces. The solver is particularly suitable for dynamical mean-field theory in circumstances where quantum Monte Carlo approaches are ineffective. It exploits the sparsity…
A well-established method to deal with highly correlated systems is based on the expansion of the Green's function in terms of spectral moments. In the context of the Composite Operator Method one approximation is proposed: a set of n…
In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…
We introduce the projected Green's function technique to study quasi-periodic systems such as the Andre-Aubry-Harper (AAH) model and beyond. In particular, we use projected Green's functions to construct a "rational approximate" sequence of…
Balanced truncation, a technique from robust control theory, is a systematic method for producing simple approximate models of complex linear systems. This technique may have significant applications in physics, particularly in the study of…