Spin entanglement in atoms and molecules

We investigate the effects of inhomogeneities on spin entanglement in many-electron systems from an ab-initio approach. The key quantity in our approach is the local spin entanglement length, which is derived from the local concurrence of the electronic system. Although the concurrence for an interacting systems is a highly nonlocal functional of the density, it does have a simple, albeit approximate expression in terms of Kohn-Sham orbitals. We show that the electron localization function -- well known in quantum chemistry as a descriptor of atomic shells and molecular bonds -- can be reinterpreted in terms of the ratio of the local entanglement length of the inhomogeneous system to the entanglement length of a homogenous system at the same density. We find that the spin entanglement is remarkably enhanced in atomic shells and molecular bonds.

Large two-dimensional electronic systems: Self-consistent energies and densities at low cost

We derive a self-consistent local variant of the Thomas-Fermi approximation for (quasi-)two-dimensional (2D) systems by localizing the Hartree term. The scheme results in an explicit orbital-free representation of the electron density and energy in terms of the external potential, the number of electrons, and the chemical potential determined upon normalization. We test the method over a variety 2D nanostructures by comparing to the Kohn-Sham 2D-LDA calculations up to 600 electrons. Accurate results are obtained in view of the negligible computational cost. We also assess a local upper bound for the Hartree energy.

Phononic Self energy effects and superconductivity in CaC$_6$

We study the graphite intercalated compound CaC$_6$ by means of Eliashberg theory, focusing on the anisotropy properties. An analysis of the electron-phonon coupling is performed, and we define a minimal 6-band anisotropy structure. Comparing with Superconducting Density Functional Theory (SCDFT) the condition under which Eliashberg theory is able to reproduce the SCDFT gap structure is determined, and we discuss the role of Coulomb interactions. The Engelsberg-Schrieffer polaron structure is computed by solving the Eliashberg equation on the Matsubara axis and analytically continuing it to the full complex plane. This reveals the polaronic quasiparticle bands anisotropic features as well as the interplay with superconductivity.

Exact conditions and scaling relations in finite temperature density functional theory

Finite temperature density functional theory provides, in principle, an exact description of the thermodynamical equilibrium of many-electron systems. In practical applications, however, the functionals must be approximated. Efficient and physically meaningful approximations can be developed if relevant properties of the exact functionals are known and taken into consideration as constraints. In this work, derivations of exact properties and scaling relations for the main quantities of finite temperature density functional theory are presented. In particular, a coordinate scaling transformation at finite temperature is introduced and its consequences are elucidated.

Parameter-free density functional for the correlation energy in two dimensions

Accurate treatment of the electronic correlation in inhomogeneous electronic systems, combined with the ability to capture the correlation energy of the homogeneous electron gas, allows to reach high predictive power in the application of density-functional theory. For two-dimensional systems we can achieve this goal by generalizing our previous approximation [Phys. Rev. B 79, 085316 (2009)] to a parameter-free form, which reproduces the correlation energy of the homogeneous gas while preserving the ability to deal with inhomogeneous systems. The resulting functional is shown to be very accurate for finite systems with an arbitrary number of electrons with respect to numerically exact reference data.

On the lower bound on the exchange-correlation energy in two dimensions

We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature.

Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions

Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasi-one dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained, and give evidence of an interesting dimensional crossover between two and one dimensions.