Related papers: Calculating Feynman diagrams with matrix product s…
In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…
We present the results of a Wilson Renormalization Group study of the single-impurity Kondo and Anderson models in a system with a gap in the conduction electron spectrum. The behavior of the impurity susceptibility and the zero-frequency…
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…
Chord diagrams and combinatorics of word algebras are used to model products of Dirac matrices, their traces, and contractions. A simple formula for the result of arbitrary contractions is derived, simplifying and extending an old…
We study the effect of electron correlations on a system consisting of a single-level quantum dot with local Coulomb interaction attached to two superconducting leads. We use the single-impurity Anderson model with BCS superconducting baths…
This article describes three Mathematica packages for the automatic calculation of one-loop Feynman diagrams: the diagrams are generated with FeynArts, algebraically simplified with FormCalc, and finally evaluated numerically using the…
We discuss the evaluation of the integrals for intermediate-order diagrams in the self-consistent strong-coupling expansion on the Keldysh contour using Tensor Cross Interpolation (TCI). TCI is used to factorize the nested parts of the…
We designed new algorithms for summing bold-line Feynman diagrams in arbitrary channels, where it can be readily modified for bare interaction series as well. When applied to magnetic channel bold-line series with on-site Hubbard…
We develop a numerically exact scheme for resumming certain classes of Feynman diagrams in the self-consistent perturbation expansion for the electron and magnon self-energies in the nonequilibrium Green function formalism applied to a…
Within the recently introduced auxiliary master equation approach it is possible to address steady state properties of strongly correlated impurity models, small molecules or clusters efficiently and with high accuracy. It is particularly…
Electron tunneling through a system formed by two coupled quantum dots in a parallel geometry is considered within a generalized Anderson model. The dots are assumed to have nearly equal radii but different (and tunable) gate voltages. In…
The generating series of the intersection numbers of the stable cohomology classes on moduli spaces of curves satisfies the string equation and a KdV hierarchy. Kontsevich's original proof of this result uses a matrix model and the matrix…
Using integration by parts relations, Feynman integrals can be represented in terms of coupled systems of differential equations. In the following we suppose that the unknown Feynman integrals can be given in power series representations,…
The two point integrals contributing to the self energy of a particle in a three dimensional quantum field theory are calculated to two loop order in perturbation theory as well as the vacuum ones contributing to the effective potential to…
Recent experimental advances in scanning tunneling microscopy make the measurement of the conductance spectra of isolated and magnetically coupled atoms on nonmagnetic substrates possible. Notably these spectra are characterized by a…
We present a numerically exact steady-state inchworm Monte Carlo method for nonequilibrium quantum impurity models. Rather than propagating an initial state to long times, the method is directly formulated in the steady-state. This…
The theory of correlated electron systems is formulated in a form which allows to use as a reference point an ab initio band structure theory (AIBST). The theory is constructed in two steps. As a first step the total Hamiltonian is…
Two-loop vertex Feynman diagrams with infrared and collinear divergences are investigated by two independent methods. On the one hand, a method of calculating Feynman diagrams from their small momentum expansion extended to diagrams with…
We reexamine basic aspects of a nonequilibrium steady state in the Kondo problem for a quantum dot under a bias voltage using a reduced density matrix, which is obtained in the Fock space by integrating out one of the two conduction…
The free energy of a field theory can be considered as a functional of the free correlation function. As such it obeys a nonlinear functional differential equation which can be turned into a recursion relation. This is solved order by order…