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We introduce a generic and accessible implementation of an exact diagonalization method for studying few-fermion models. Our aim is to provide a testbed for the newcomers to the field as well as a stepping stone for trying out novel…
A number of methods are discussed which may serve for a treatment of electron correlations in solids. When the electron correlations are relatively weak like in semiconductors or a number of ionic crystals one may start from a…
In Nuclear Physics numerous possibilities exist to investigate fundamental symmetries and interactions. In particular, the precise measurements of properties of fundamental fermions, searches for new interactions in $\beta$-decays, and…
Solid state theory, density functional theory and its generalizations for correlated systems together with numerical simulations on supercomputers allow nowadays to model magnetic systems realistically and in detail and can be even used to…
The dynamics of many-body fermionic systems are important in problems ranging from catalytic reactions at electrochemical surfaces, to transport through nanojunctions, and offer a prime target for quantum computing applications. Here we…
We have studied quasi one-dimensional few-particle systems consisting of one to six ultracold fermionic atoms in two different spin states with attractive interactions. We probe the system by deforming the trapping potential and by…
We introduce a density functional formalism to study the ground-state properties of strongly-correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling…
Ultracold atomic systems offer a unique tool for understanding behavior of matter in the quantum degenerate regime, promising studies of a vast range of phenomena covering many disciplines from condensed matter to quantum information and…
Strongly interacting fermions define the properties of complex matter at all densities, from atomic nuclei to modern solid state materials and neutron stars. Ultracold atomic Fermi gases have emerged as a pristine platform for the study of…
We offer a unified treatment of distinct measures of well-posedness for homogeneous conic systems. To that end, we introduce a distance to infeasibility based entirely on geometric considerations of the elements defining the conic system.…
Most approximate exchange-correlation functionals used within density functional theory are constructed as the sum of two distinct contributions for exchange and correlation. Separating the exchange component from the entire functional is…
We present a new approach for the quantification of quantumness of correlations in fermionic systems. We study the Multipartite Relative Entropy of Quantumness in such systems, and show how the symmetries in the states can be used to obtain…
A novel approach to electronic correlations in magnetic crystals which takes into account a dynamical many-body effects is present. In order to to find a frequency dependence of the electron self energy, an effective quantum-impurity…
We develop a discrete fermion approach for modelling the strong interaction of an arbitrary system interacting with continuum electronic reservoirs. The approach is based on a pseudo-fermion decomposition of the continuum bath correlation…
An exponential interaction is constructed so that one-dimensional atoms and chains of atoms mimic the general behavior of their three-dimensional counterparts. Relative to the more commonly used soft-Coulomb interaction, the exponential…
Electron-electron interactions are at the origin of many exotic electronic properties of materials which have emerged from recent experimental observations. The main important phenomena discovered are related with electronic magnetic…
The notion of "paired" fermions is central to important condensed matter phenomena such as superconductivity and superfluidity. While the concept is widely used and its physical meaning is clear there exists no systematic and mathematical…
In this chapter we focus first on the theoretical methods and relevant computational approaches to calculate the electronic structure of atoms, molecules, and clusters containing heavy elements for which relativistic effects become…
We derive an exact representation of the exchange-correlation energy within density functional theory (DFT) which spawns a class of approximations leading to correct long-range asymptotic behavior. In what amounts to be the simplest…
The symmetric (Heisenberg) exchange interaction is fundamental to magnetism and assumes critical importance in designing magnetic materials for novel emergent phenomena and device applications. However, quantifying exchange is extremely…