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We propose a simple Hamiltonian to describe the motion and the merging of Dirac points in the electronic spectrum of two-dimensional electrons. This merging is a topological transition which separates a semi-metallic phase with two Dirac…
An effective Hamiltonian is derived in the case of the strong Hund coupling and on-site Coulomb interaction by means of a projective perturbation approach. A physical mechanism for charge ordering in half-doped manganites…
We present a precise fully relativistic numerical solution of the two-center Coulomb problem. The special case of unit nuclear charges is relevant for the accurate description of the ${\rm H}_2^+$ molecular ion and its isotopologues,…
Radical-ion pairs, fundamental for understanding photosynthesis and the avian magnetic compass, were recently shown to be biological open quantum systems. We here show that the coupling of the radical-pair's spin degrees of freedom to its…
By a combination of Monte Carlo simulations and analytical calculations, we investigate the effective interactions between highly charged planar interfaces, neutralized by mobile counterions (salt-free system). While most previous analysis…
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once…
The Douglas-Kroll transformed Dirac-Coulomb Hamiltonian is used to describe scalar-relativistic effects in solids. A Hartree-Fock approximation with periodic boundary conditions makes it feasible to use methods originally developed for…
We report on a study of interaction effects on the polarization of a disordered two-dimensional electron system in a strong magnetic field. Treating the Coulomb interaction within the time-dependent Hartree-Fock approximation we find…
We study the quantum criticality of the phase transition between the Dirac semimetal and the excitonic insulator in two dimensions. Even though the system has a semimetallic ground state, there are observable effects of excitonic pairing at…
The hydrogen atom with the Coulomb interaction is one of the exactly solvable non-relativistic quantum models. Unlike many other exactly solvable models it describes a real physical object providing the formulas for energy levels and…
We investigate the interplay between confinement and the fermion doubling problem in Dirac-like Hamiltonians. Individually, both features are well known. First, simple electrostatic gates do not confine electrons due to the Klein tunneling.…
The effects of intrinsic spin-orbit and Coulomb interactions on low-energy properties of finite width graphene armchair ribbons are studied by means of a Dirac Hamiltonian. It is shown that metallic states subsist in the presence of…
The mechanism of the Coulomb breakup reactions of the nuclei with neutron-halo structure is investigated in detail. A time-dependent Schr\"odinger equation for the halo neutron is numerically solved by treating the Coulomb field of a target…
The second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schr\"odinger perturbation theory, with the use of the Sturmian series expansion of the generalized…
Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize, thereby reducing the magnitude of the interaction. Exchange integrals of…
Tight binding electrons on a honeycomb lattice are described by an effective Dirac theory at low energies. Lowering symmetry by an alternate ionic potential ($\Delta$) generates a single-particle gap in the spectrum. We employ the dynamical…
A simple analytical solution is found to the Dirac equation for the combination of a Coulomb potential with a linear confining potential. An appropriate linear combination of Lorentz scalar and vector linear potentials, with the scalar part…
Understanding the quantum dynamics of spin defects and their coherence properties requires accurate modeling of spin-spin interaction in solids and molecules, for example by using spin Hamiltonians with parameters obtained from…
We investigate the effects of long range Coulomb interactions on the low-temperature properties of a second-order Dirac semimetal in terms of the renormalization group. In contrast to the first-order Dirac semimetal, the full rotation…
We construct a solution to the equation of motion of Hamiltonian lattice QCD in the strong coupling limit using Wilson fermions which exactly diagonalizes the Hamiltonian to second order in the field operators. This solution obeys the free…