Related papers: Machine learning for many-body physics: The case o…
A review of electronic dynamics of single-impurity and many-impurity Anderson models is contained in this report. Those models are used widely for many of the applications in diverse fields of interest, such as surface physics, theory of…
Quantum many-body methods provide a systematic route to computing electronic properties of molecules and materials, but high computational costs restrict their use in large-scale applications. Due to the complexity in many-electron…
Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an…
Solving the Anderson impurity model typically involves a two-step process, where one first calculates the ground state of the Hamiltonian, and then computes its dynamical properties to obtain the Green's function. Here we propose a hybrid…
The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We…
The description of the dynamics of correlated electrons in quantum impurity models is typically described within the nonequilibrium Green function formalism combined with a suitable approximation. One common approach is based on the…
This is an introductory chapter on how to calculate nonequilibrium Green's functions via dynamical mean-field theory for the Autumn School on Correlated Electrons: Many-Body Methods for Real Materials, 16-20 September 2019,…
This review paper describes the basic concept and technical details of sparse modeling and its applications to quantum many-body problems. Sparse modeling refers to methodologies for finding a small number of relevant parameters that well…
The Anderson Impurity Model (AIM) is a canonical model of quantum many-body physics. Here we investigate whether machine learning models, both neural networks (NN) and kernel ridge regression (KRR), can accurately predict the AIM spectral…
Generalized quantum impurity models -- which feature a few localized and strongly-correlated degrees of freedom coupled to itinerant conduction electrons -- describe diverse physical systems, from magnetic moments in metals to…
We provide a mathematical analysis of the Dynamical Mean-Field Theory, a celebrated representative of a class of approximations in quantum mechanics known as embedding methods. We start by a pedagogical and self-contained mathematical…
We derive equations of motion for higher order density response functions using the theory of thermodynamic Green's functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions.…
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…
The strong electron correlations caused by Coulomb interaction of impurity electrons are taken into account. The infinite series of diagrams containing irreducible Green's functions are summed. For symmetric Anderson model we establish the…
We address the problem of analytic continuation of imaginary-frequency Green's functions, which is crucial in many-body physics, using machine learning based on a multi-level residual neural network. We specifically address potential biases…
Machine learning opens new avenues for modelling correlated materials. Quantum embedding approaches, such as the dynamical mean-field theory (DMFT), provide corrections to first-principles calculations for strongly correlated materials,…
We present a machine-learning approach to a long-standing issue in quantum many-body physics, namely, analytic continuation. This notorious ill-conditioned problem of obtaining spectral function from imaginary time Green's function has been…
Nonperturbative dynamic theory has a particular advantage in studying the transport in a quantum impurity system in a steady state. Here, we develop a new approach for obtaining the retarded Green's function expressed in resolvent form. We…
A state-of-the-art method that combines a quantum computational algorithm and machine learning, so-called quantum machine learning, can be a powerful approach for solving quantum many-body problems. However, the research scope in the field…
In this article we formulate the superperturbation theory for the Anderson impurity model on the real axis. The resulting impurity solver allows to evaluate dynamical quantities without numerical analytical continuation by the maximum…