Related papers: Algorithmic Matsubara Integration for Hubbard-like…
Feynman diagrams may be evaluated by Mellin-Barnes representations of their Feynman parameter integrals in d=4-2\eps dimensions. Recently, the Mathematica toolkit AMBRE has been developed for the automatic derivation of such representations…
The asymmetric Hubbard model is used in investigating the lattice gas of the moving particles of two types. The model is considered within the dynamical mean-field method. The effective single-site problem is formulated in terms of the…
In numerical simulations, spontaneously broken symmetry is often detected by computing two-point correlation functions of the appropriate local order parameter. This approach, however, computes the square of the local order parameter, and…
The hierarchical equations of motion (HEOM), derived from the exact Feynman-Vernon path integral, is one of the most powerful numerical methods to simulate the dynamics of open quantum systems that are embedded in thermal environments.…
A systematically improvable wave function is proposed for the numerical solution of strongly correlated systems. With a stochastic optimization method, based on the auxiliary field quantum Monte Carlo technique, an effective temperature…
Given a connected (multi)graph G, consisting of V vertices and I lines, we consider a class of multidimensional sums constructed in the following way: - orient the lines of the graph in some (arbitrary) fashion - assign to each line i a…
We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we…
The model of a strongly correlated system in which periodically spaced Anderson-Hubbard centers are introduced into narrow-band metal is considered. Besides the interactions between localized magnetic moments and strong on-site Coulomb…
We compute the diagrammatic expansion of the particle-particle susceptibility via algorithmic Matsubara integration and compute the correlated pairing susceptibility in the thermodynamic limit of the 2D Hubbard Model. We study the static…
The functional integral method can be used in quantum mechanics to find the scattering amplitude for particles in the external field. We will obtain the potential scattering amplitude form the complete Green function in the corresponding…
We present a quantum Monte Carlo method which allows calculations on many-fermion systems at finite temperatures without any sign decay. This enables simulations of the grand-canonical ensemble at large system sizes and low temperatures.…
These notes are intended as a detailed discussion on how to implement the diagrammatic Monte Carlo method for a physical system which is technically simple and where it works extremely well, namely the Fr\"ohlich polaron problem. Sampling…
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…
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 introduce a new method to evaluate algebraic integrals over the simplex numerically. This new approach employs techniques from tropical geometry and exceeds the capabilities of existing numerical methods by an order of magnitude. The…
We present a simple technique that allows to generate Feynman diagrams for vector models with interactions of order $2n$ and similar models (Gross-Neveu, Thirring model), using a bootstrap equation that uses only the free field value of the…
We introduce diagrammatic technique for Hubbard nonequilibrium Green functions (NEGF). The formulation is an extension of equilibrium considerations for strongly correlated lattice models to description of current carrying molecular…
The 'Neumann-Ulam' Monte-Carlo sampling is described for the calculation of a matrix inversion or a Green function in case of Hubbard-Stratonovich (HS-)transformed coherent state path integrals. We illustrate how to circumvent direct…
We introduce a diagrammatic multi-scale approach to the Hubbard model based on the interaction-irreducible (multi-boson) vertex of a small cluster embedded in a self-consistent medium. The vertex captures short-ranged correlations up to the…
In many field theoretical models one has to resum two- and four-legged subdiagrams in order to determine their behaviour. In this article we present a novel formalism which does this in a nice way. It is based on the central limit theorem…