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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 show how to use diagrammatic techniques to compute the weak-coupling perturbation series of the self-consistent solution to a Dynamical Mean Field Theory (DMFT) problem. This approach constitutes an alternative to using diagrammatic…
We review recent progress in our theoretical understanding of strongly correlated fermion systems in the presence of disorder. Results were obtained by the application of a powerful nonperturbative approach, the Dynamical Mean-Field Theory…
Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…
The DFT calculations were performed of densities of states of semiconductor GaAs and magnetic semiconductor Ga0.9375Mn0.0625As. It is obtained that a part of Mn3d- states is hybridized with valence band at Fermi level. The exchange…
The quantum-mechanical problem of a many-particle system with a single impurity in one-dimension, interacting by a delta-function, is solved. The wave-function for a bosonic system and the related secular equation for the spectrum are…
Strongly correlated quantum impurity problems appear in a wide variety of contexts ranging from nanoscience and surface physics to material science and the theory of strongly correlated lattice models, where they appear as auxiliary systems…
We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements…
We present a generalization of the Time Dependent Variational Principle (TDVP) to any finite sized loop-free tensor network. The major advantage of TDVP is that it can be employed as long as a representation of the Hamiltonian in the same…
The one-dimensional problem of $N$ particles with contact interaction in the presence of a tunable transmitting and reflecting impurity is investigated along the lines of the coordinate Bethe ansatz. As a result, the system is shown to be…
The accurate prediction of the electronic properties of materials at a low computational expense is a necessary conditions for the development of effective high-throughput quantum-mechanics (HTQM) frameworks for accelerated materials…
Tensor network methods as presented in our open source Matrix Product States software have opened up the possibility to study many-body quantum physics in one and quasi-one-dimensional systems in an easily accessible package similar to…
A new numerical method for the solution of the Dynamical Mean Field Theory's self-consistent equations is introduced. The method uses the Density Matrix Renormalization Group technique to solve the associated impurity problem. The new…
Multi-orbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to…
We extend the natural orbital impurity solver [PRB 90, 085102 (2014)] to finite temperatures and apply it to calculate spectral and transport properties of correlated electrons within the dynamical mean-field theory. First, we benchmark our…
The self consistent version of the density functional theory (DFT) is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems such as atoms, molecules and clusters. The exact functional…
We present a quantum impurity solver based on a pseudo-particle framework, which combines diagrammatic resummations for a three-point vertex with diagrammatic Monte Carlo sampling of a four-point vertex. This recently proposed approach [A.…
We developed a fast numerical algorithm for solving the three dimensional vectorial Helmholtz equation that arises in electromagnetic scattering problems. The algorithm is based on electric field integral equations and is essentially a…
The polaron problem is a very old problem in condensed matter physics that dates back to the thirties, but still remain largely unsolved today, especially when electron-electron interaction is taken into consideration. The presence of both…
The Numerical Renormalization Group is used to solve quantum impurity problems, which describe magnetic impurities in metals, nanodevices, and correlated materials within DMFT. Here we present a simple generalization of the Wilson Chain,…