arXiv subjects

S. Pittalis

Publications and source records attributed to S. Pittalis.

At least 19 recordsLinked to original sources

arXiv2018

A shortcut to gradient-corrected magnon dispersion: exchange-only case

Ab initio calculations of the magnon dispersion in ferromagnetic materials typically rely on the adiabatic local density approximation (ALDA) in which the effective exchange-correlation field is everywhere parallel to the magnetization. These calculations, however, tend to overestimate the "magnon stiffness", defined as the curvature of the magnon frequency vs. wave vector relation evaluated at zero wave vector. Here we suggest a simple procedure to improve the magnon dispersion by taking into account gradient corrections to the ALDA at the exchange-only level. We find that this gradient correction always reduces the magnon stiffness. The surprisingly large size of these corrections ($\sim 30\%$) greatly improves the agreement between the calculated and the observed magnon stiffness for cobalt and nickel, which are known to be overestimated within the ALDA.

cond-mat.mtrl-sci↗

arXiv2017

U(1)$\times$SU(2) Gauge Invariance Made Simple for Density Functional Approximations

A semi-relativistic density-functional theory that includes spin-orbit couplings and Zeeman fields on equal footing with the electromagnetic potentials, is an appealing framework to develop a unified first-principles computational approach for non-collinear magnetism, spintronics, orbitronics, and topological states. The basic variables of this theory include the paramagnetic current and the spin-current density, besides the particle and the spin density, and the corresponding exchange-correlation (xc) energy functional is invariant under local U(1)$\times$SU(2) gauge transformations. The xc-energy functional must be approximated to enable practical applications, but, contrary to the case of the standard density functional theory, finding simple approximations suited to deal with realistic atomistic inhomogeneities has been a long-standing challenge. Here, we propose a way out of this impasse by showing that approximate gauge-invariant functionals can be easily generated from existing approximate functionals of ordinary density-functional theory by applying a simple {\it minimal substitution} on the kinetic energy density, which controls the short-range behavior of the exchange hole. Our proposal opens the way to the construction of approximate, yet non-empirical functionals, which do not assume weak inhomogeneity and should therefore have a wide range of applicability in atomic, molecular and condensed matter physics.

cond-mat.mtrl-sci↗

arXiv2014

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.

quant-ph↗

arXiv2014

Construction of the B88 exchange-energy functional in two dimensions

We construct a generalized-gradient approximation for the exchange-energy density of finite two-dimensional systems. Guided by non-empirical principles, we include the proper small-gradient limit and the proper tail for the exchange-hole potential. The observed performance is superior to that of the two-dimensional local-density approximation, which underlines the usefulness of the approach in practical applications.

cond-mat.str-el↗

arXiv2013

Transverse and longitudinal gradients of the spin magnetization in Spin-Density-Functional Theory

We derive the gradient expansion for the exchange energy of a spin-polarized electron gas by perturbing the uniformly spin polarized state and thus inducing a small non-collinearity that is slowly varying in space. We show that the exchange-energy contribution due to the induced longitudinal gradient of the spin polarization to the exchange energy differs from the contribution due to the transverse gradient. The difference is present at any non-vanishing spin polarization and becomes larger with increasing spin polarization. We argue that improved generalized gradient approximations of Spin-Density-Functional Theory must account for the difference between the longitudinal and transverse spin stiffness.

cond-mat.str-el↗

arXiv2013

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.

cond-mat.str-el↗

arXiv2012

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.

cond-mat.supr-con↗

arXiv2012

Electron-Electron Interactions in Artificial Graphene

Recent advances in the creation and modulation of graphene-like systems are introducing a science of "designer Dirac materials". In its original definition, artificial graphene is a man-made nanostructure that consists of identical potential wells (quantum dots) arranged in a adjustable honeycomb lattice in the two-dimensional electron gas. As our ability to control the quality of artificial graphene samples improves, so grows the need for an accurate theory of its electronic properties, including the effects of electron-electron interactions. Here we determine those effects on the band structure and on the emergence of Dirac points.

cond-mat.str-el↗

arXiv2011

Quantum continuum mechanics in a strong magnetic field

We extend a recent formulation of quantum continuum mechanics [J. Tao et. al, Phys. Rev. Lett. {\bf 103}, 086401 (2009)] to many-body systems subjected to a magnetic field. To accomplish this, we propose a modified Lagrangian approach, in which motion of infinitesimal volume elements of the system is referred to the "quantum convective motion" that the magnetic field produces already in the ground-state of the system. In the linear approximation, this approach results in a redefinition of the elastic displacement field $\uv$, such that the particle current $\jv$ contains both an electric displacement and a magnetization contribution: $\jv=\jv_0+n_0\partial_t \uv+\nabla \times (\jv_0\times \uv)$, where $n_0$ and $\jv_0$ are the particle density and the current density of the ground-state and $\partial_t$ is the partial derivative with respect to time. In terms of this displacement, we formulate an "elastic approximation" analogous to the one proposed in the absence of magnetic field. The resulting equation of motion for $\uv$ is expressed in terms of ground-state properties -- the one-particle density matrix and the two-particle pair correlation function -- and in this form it neatly generalizes the equation obtained for vanishing magnetic field.

cond-mat.str-el↗

arXiv2011

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.

cond-mat.stat-mech↗

arXiv2010

Laplacian-level density functionals for the exchange-correlation energy of low-dimensional nanostructures

In modeling low-dimensional electronic nanostructures, the evaluation of the electron-electron interaction is a challenging task. Here we present an accurate and practical density-functional approach to the two-dimensional many-electron problem. In particular, we show that spin-density functionals in the class of meta-generalized-gradient approximations can be greatly simplified by reducing the explicit dependence on the Kohn-Sham orbitals to the dependence on the electron spin density and its spatial derivatives. Tests on various quantum-dot systems show that the overall accuracy is well preserved, if not even improved, by the modifications.

cond-mat.str-el↗

arXiv2010

Simple exchange-correlation potential with a proper long-range behavior for low-dimensional nanostructures

The exchange-correlation potentials stemming from the local-density approximation and several generalized-gradient approximations are known to have incorrect asymptotic decay. This failure is independent of the dimensionality, but so far the problem has been corrected -- within the mentioned approximations -- only in three dimensions. Here we provide a cured exchange-correlation potential in two dimensions, where the applications have a continuously increasing range in, e.g., semiconductor physics. The given potential is a generalized-gradient approximation, which is as easy to apply as the local-density approximation. We demonstrate that the corrected potential agrees very well with the analytic result of a two-electron quantum dot in the asymptotic regime, and yields plausible exchange-correlation potentials for larger two-dimensional systems.

cond-mat.str-el↗

arXiv2010

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.

cond-mat.str-el↗

arXiv2010

Anti-adiabatic limit of the exchange-correlation kernels of an inhomogeneous electron gas

We express the high-frequency (anti-adiabatic) limit of the exchange-correlation kernels of an inhomogeneous electron gas in terms of the following equilibrium properties: the ground-state density, the kinetic stress tensor, the pair-correlation function, and the ground-state exchange-correlation potential. Of these quantities, the first three are amenable to exact evaluation by Quantum Monte Carlo methods, while the last can be obtained from the inversion of the Kohn-Sham equation for the ground-state orbitals. The exact scalar kernel, in this limit, is found to be of very long range in space, at variance with the kernel that is used in the standard local density approximation. The anti-adiabatic xc kernels should be useful in calculations of excitation energies by time-dependent DFT in atoms, molecules, and solids, and provides a solid basis for interpolation between the low- and high-frequency limits of the xc kernels.

cond-mat.str-el↗

arXiv2010

Universal correction for the Becke-Johnson exchange potential

The Becke-Johnson exchange potential [J. Chem. Phys. 124, 221101 (2006)] has been successfully used in electronic structure calculations within density-functional theory. However, in its original form the potential may dramatically fail in systems with non-Coulombic external potentials, or in the presence of external magnetic or electric fields. Here, we provide a system-independent correction to the Becke-Johnson approximation by (i) enforcing its gauge invariance and (ii) making it exact for any single-electron system. The resulting approximation is then better designed to deal with current-carrying states, and recovers the correct asymptotic behavior for systems with any number of electrons. Tests of the resulting corrected exchange potential show very good results for a Hydrogen chain in an electric field and for a four-electron harmonium in a magnetic field.

cond-mat.mtrl-sci↗

arXiv2010

Semi-local density functional for the exchange-correlation energy of electrons in two dimensions

We present a practical and accurate density functional for the exchange-correlation energy of electrons in two dimensions. The exchange part is based on a recent two-dimensional generalized-gradient approximation derived by considering the limits of small and large density gradients. The fully local correlation part is constructed following the Colle-Salvetti scheme and a Gaussian approximation for the pair density. The combination of these expressions is shown to provide an efficient density functional to calculate the total energies of two-dimensional electron systems such as semiconductor quantum dots. Excellent performance of the functional with respect to numerically exact reference data for quantum dots is demonstrated.

cond-mat.str-el↗

arXiv2009

Exchange and correlation energy functionals for two-dimensional open-shell systems

We consider density functionals for exchange and correlation energies in two-dimensional systems. The functionals are constructed by making use of exact constraints for the angular averages of the corresponding exchange and correlation holes, respectively, and assuming proportionality between their characteristic sizes. The electron current and spin are explicitly taken into account, so that the resulting functionals are suitable to deal with systems exhibiting orbital currents and/or spin polarization. Our numerical results show that in finite systems the proposed functionals outperform the standard two-dimensional local spin-density approximation, still performing well also in the important limit of the homogeneous two-dimensional electron gas.

cond-mat.str-el↗

arXiv2009

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.

cond-mat.str-el↗