Related papers: irbasis: Open-source database and software for int…
Information compression plays a central role in diverse fields of modern science and technology, from communication theory to machine learning. In condensed-matter physics, the intermediate representation (IR) basis has recently been…
This lecture note reviews recently proposed sparse-modeling approaches for efficient ab initio many-body calculations based on the data compression of Green's functions. The sparse-modeling techniques are based on a compact orthogonal…
New model-independent compact representations of imaginary-time data are presented in terms of the intermediate representation (IR) of analytical continuation. This is motivated by a recent numerical finding by the authors [J. Otsuki et…
We present an efficient basis for imaginary time Green's functions based on a low rank decomposition of the spectral Lehmann representation. The basis functions are simply a set of well-chosen exponentials, so the corresponding expansion…
The imaginary-time Green's function is a building block of various numerical methods for correlated electron systems. Recently, it was shown that a model-independent compact orthogonal representation of the Green's function can be…
Inspired by the recent proposed Legendre orthogonal polynomial representation of imaginary-time Green's functions, we develop an alternate representation for the Green's functions of quantum impurity models and combine it with the…
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…
We study the expansion of single-particle and two-particle imaginary-time Matsubara Green's functions of quantum impurity models in the basis of Legendre orthogonal polynomials. We discuss various applications within the dynamical…
We introduce libdlr, a library implementing the recently introduced discrete Lehmann representation (DLR) of imaginary time Green's functions. The DLR basis consists of a collection of exponentials chosen by the interpolative decomposition…
Efficient ab initio calculations of correlated materials at finite temperature require compact representations of the Green's functions both in imaginary time and Matsubara frequency. In this paper, we introduce a general procedure which…
The Matsubara Green's function formalism stands as a powerful technique for computing the thermodynamic characteristics of interacting quantum many-particle systems at finite temperatures. In this manuscript, our focus centers on…
The temperature-dependent Matsubara Green's function that is used to describe temperature-dependent behavior is expressed on a numerical grid. While such a grid usually has a couple of hundred points for low-energy model systems, for…
Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size and discontinuity structure, they are challenging to handle numerically. Recently, two advances were…
In this work, we present a mesh-independent, data-driven library, chebgreen, to mathematically model one-dimensional systems, possessing an associated control parameter, and whose governing partial differential equation is unknown. The…
Analytic continuation is a critical step in quantum many-body computations, connecting imaginary-time or Matsubara Green's functions with real-frequency spectral functions, which can be directly compared to experimental results. However,…
In this article we use linear algebra to improve the computational time for the obtaining of Green's functions of linear differential equations with reflection (DER). This is achieved by decomposing both the `reduced' equation (the ODE…
Green's function methods lead to ab initio, systematically improvable simulations of molecules and materials while providing access to multiple experimentally observable properties such as the density of states and the spectral function.…
Quantitative descriptions of strongly correlated materials pose a considerable challenge in condensed matter physics and chemistry. A promising approach to address this problem is quantum embedding methods. In particular, the dynamical…
By exploiting the analyticity and boundary value properties of the thermal Green functions that result from the KMS condition in both time and energy complex variables, we treat the general (non-perturbative) problem of recovering the…
The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate…