Nonadiabatic Exchange-Correlation Potential for Strongly Correlated Materials in the Weak and Strong Interaction Limits

I review recent advances in understanding the physical character of the exchange-correlation (xc) potential in time-dependent density functional theory. I show that in an electron gas of slowly varying density the dynamical part of the xc potential is an extremely nonlocal functional of the density. This difficulty can be circumvented by introducing an xc vector potential that is a function of the local current density. The form of this vector potential is entirely specified by symmetry. Its physical effects are analogous to those of the viscous force in the Navier-Stokes equation of classical hydrodynamics. Recent applications of the xc vector potential to the calculation of infrared absorption linewidths in quantum wells are described.

It is shown that the exchange-correlation part of the action functional\n$A_{xc}[\\rho (\\vec r,t)]$ in time-dependent density functional theory , where\n$\\rho (\\vec r,t)$ is the time-dependent density, is invariant under the\ntransformation to an accelerated frame of reference $\\rho (\\vec r,t) \\to \\rho '\n(\\vec r,t) = \\rho (\\vec r + \\vec x (t),t)$, where $\\vec x (t)$ is an arbitrary\nfunction of time. This invariance implies that the exchange-correlation\npotential in the Kohn-Sham equation transforms in the following manner:\n$V_{xc}[\\rho '; \\vec r, t] = V_{xc}[\\rho; \\vec r + \\vec x (t),t]$. Some of the\napproximate formulas that have been proposed for $V_{xc}$ satisfy this exact\ntransformation property, others do not. Those which transform in the correct\nmanner automatically satisfy the ``harmonic potential theorem", i.e. the\nseparation of the center of mass motion for a system of interacting particles\nin the presence of a harmonic external potential. A general method to generate\nfunctionals which possess the correct symmetry is proposed.\n

Time-dependent density-functional methods are used to compute excitation energies and, via the adiabatic-connection fluctuation-dissipation theorem, ground-state correlation energies of atoms, ions, and the H${}_{2}$ molecule at various bond lengths. Various exchange-correlation potentials ${v}_{xc}$ and exchange-correlation kernels ${f}_{xc}$ are tested. Accurate exchange-correlation potentials are found to be essential for getting accurate energies. Methods employing in the Kohn-Sham self-consistency process the exact local Kohn-Sham exchange potential while neglecting completely the correlation potential lead to better excitation and correlation energies than methods with exchange-correlation potentials within the local density approximation or the generalized gradient approximation. Taking into account the exact exchange-correlation potential and thus the exact Kohn-Sham potential further improves excitation and correlation energies.

We analyze the effects of electron correlations and memory in high harmonic generation from BiFeO3 using Dynamical Mean-Field Theory and Time-Dependent Density-Functional Theory. We observe both effects lead to an extension of the harmonic cutoff.

Time-Dependent Density-Functional Theory (TDDFT) has become a promising alternative to the Bethe-Salpeter Equation (BSE) in terms of the calculation of optical spectra, including excitoinic features, due to its significantly lower computational cost. TDDFT brings with it the advantage of, in principle, access to the Time-Dependent (TD) exciton wave function and the ability to study ultra-fast TD phenomena. One promising family of Exchange & Correlation (XC) functionals for capturing excitonic effects in TDDFT are the Long-Range Corrected (LRC) functionals. In order to test the LRC functionals, we have written programs to do calculations in both a One-Dimensional (1D) and Two-Dimensional (2D) model systems. We used the 1D model system to explore avenues of TD exciton wave function visualization to facilitate the study and understanding of the TD dynamics of excitons. Likewise, we used the 2D model system to study various methods of correction to the LRC in hopes of better capturing excitonic effects and improving stability for Real-Time (RT) calculations. We show examples of exciton wave functions visualized with various techniques, including waterfall plots and heat maps. We have also used our 1D model system to explore how RT calculations performed using TDDFT can be used to gain insight into novel systems, as exemplified by our study of charge-transfer excitations. Using our 2D model system we have explored two possible avenues of correction to the LRC: adding a 'counter' term to the XC functional and 'generalizing' the differential equation which defines the LRC. The first avenue we explored is the addition of a new term to the XC potential, explicitly constructed to cancel out the error produced by the LRC's violation of the zero-force theorem, leading to the introduction of spurious, nonphysical, internal forces. This approach, in the end, does not seem to make a substantial impact on the optical absorption spectra or the stability of the LRC. The second avenue, using the so-called "Proca" equation, adds terms to the equation of motion in order to stabilize the calculations-again with limited success. We have successfully demonstrated in our model systems that the RT methods for TDDFT are promising tools for the exploration of TD phenomena in electronic systems. We have also explored these techniques using some illustrative situations and avenues for improving the accuracy and stability of these calculations.

We study the origin of in-plane ferromagnetism in monolayer VSe2 focusing on the effect of charge doping and mechanical strain. We start from an anisotropic spin Hamiltonian, estimate its parameters from density functional calculations, and determine the spectrum of spin-wave excitations. We show that 1T-VSe2 is characterized by relatively strong on-site Coulomb repulsion (U ≃ 5 eV), favoring an antiferromagnetic ground state, which contradicts experimental observations. We calculate the magnetic phase diagram as a function of charge doping and strain, and find a transition to the ferromagnetic state with in-plane easy axis under moderate hole doping (∼1014 cm−2). Analysis of spin-wave excitations in doped monolayer VSe2 reveals a gap due to the in-plane anisotropy, giving rise to long-range magnetic order well above 300 K, in agreement with recent experiments. Our findings suggest that experimentally available 1T-VSe2 monolayer samples might be intrinsically or extrinsically doped, which opens up the possibility for a controllable manipulation of their magnetic properties.

We show that interference between parallel currents through two quantum dots, in presence of spin orbit interactions and strong on-site Coulomb repulsion, leads to resonances in current noise at the corresponding Larmor frequencies. An additional resonance at the difference of Larmor frequencies is present even without spin-orbit interaction. The resonance lines have strength comparable to the background shot noise and therefore can account for the numerous observations of spin resonance in STM noise with non-polarized leads. We solve also several other models that show similar resonances.

First-principles investigation has been carried out in order to analyze structural, electronic, and magnetic properties of RESn3 compounds, thereby exploiting specific properties for better understanding of their magnetic structure. The generalized gradient approximation + U formalism has been used to account for the strong on-site Coulomb repulsion among the localized RE 4 f electrons. By varying the Hubbard U parameter from 0 to 8 eV, a detailed study of magnetism of these compounds via the density of states DOS and charge densities, is presented.

Semiconductor surfaces with narrow surface bands provide unique playgrounds to search for Mott-insulating state. Recently, a combined experimental and theoretical study of the two-dimensional (2D) Sn atom lattice on a wide-gap SiC(0001) substrate proposed a Mott-type insulator driven by strong on-site Coulomb repulsion U within a single-band Hubbard model. However, our systematic density-functional theory (DFT) study with local, semilocal, and hybrid exchange-correlation functionals shows that the Sn dangling-bond state largely hybridizes with the substrate Si 3p and C 2p states to split into three surface bands due to the crystal field. Such a hybridization gives rise to the stabilization of the antiferromagnetic order via superexchange interactions. The band gap and the density of states predicted by the hybrid DFT calculation agree well with photoemission data. Our findings not only suggest that the Sn/SiC(0001) system can be represented as a Slater-type insulator driven by long-range magnetism, but also have an implication that taking into account long-range interactions beyond the on-site interaction would be of importance for properly describing the insulating nature of Sn/SiC(0001).

The influence of external magnetic field h on a static conductivity of MottHubbard material which is described by model with correlated hopping of electrons has been investigated. By means of canonical transformation the effective Hamiltonian which takes into account strong intra-site Coulomb repulsion and correlated hopping is obtained. Using a variant of generalized Hartree-Fock approximation the single-electron Green function and quasiparticle energy spectrum of the model have been calculated. The static conductivity σ has been calculated as a function of h, electron concentration n and temperature T . The correlated hopping is shown to cause the electron-hole asymmetry of transport properties of narrow band materials. keywordsMott-Hubbard material, conductivity, magnetic field pacs72.15-v; 72.80.Ga. The achievements of the recent years in the field of strongly correlated electron systems give us the opportunity to understand the properties of narrow-band materials, in particular those in which metal-insulator transition under the action of external influences (pressure, doping, temperature) is realized [1]. The strongly correlated electron systems demonstrate unusual transport properties [2]. For understanding of the physical mechanisms, which cause these peculiarities, the experimental and theoretical researches of the temperature dependence of conductivity are needed. The results concerning low-frequency behavior of conductivity are of the prior importance, because it gives the information about the scattering processes close to the Fermi surface. The theoretical investigation of conductivity σ(ω, T ) are mainly concentrated in the limit T = 0. Behavior of the static conductivity σ(T ) = σ(ω = 0, T ) at T > 0 has not been studied sufficiently. Theoretical investigations of the optical conductivity in the Hubbard model [3] in the frameworks of the Kubo linear response theory [4] last for many decades, we note here the investigations by analytical methods: moment method [5], in composite operators method [6], in the mean-field theory [7, 8], in the perturbative theory method [9, 10] in the limit of weak interaction (|t| ≫ U), in method of the memory function [11, 12], in the opposite limit (U ≫ |t|). The conductivity has been intensively studied in onedimensional Hubbard model [13]-[15], where the numerical results can be compared with exact ones obtained by Bethe ansatz application.

The time dependence of the exchange-correlation energy in density functional theory is given in terms of the exchange-correlation potential. The virial theorem for the exchange-correlation potential is shown to hold for time-dependent electronic systems and is illustrated by an exactly solved model: Hooke’s atom with a time-dependent force constant. A relation between the coupling constant and functionals evaluated on scaled densities is derived. [S0031-9007(98)08169-1]

Strong-field ionization of Li and Be: a time-dependent density functional theory with self-interaction correction

When a molecular system is subjected to an external electric perturbation, originating from an electromagnetic wave or from a charged moving particle (in molecule-ion collisions), the electrons are the first particles to respond, on the attosecond timescale. Electron dynamics (ED) can be simulated by so-called real-time time-dependent density functional theory (RT-TDDFT). Within this framework, ED is driven by the electrostatic potential and by exchange-correlation potentials that fluctuate on the attosecond time scale. In vacuum the speed of light approaches 3 A as−1. Therefore, when simulating ED in extended molecular systems the question of retardation in the propagation of the potentials has to be posed. In this contribution we investigate two types of retardation; the first one deals with retardation in the potential created by a collision with a charged projectile. This is done through the Lienard-Wiechert potential (LWP). The second one deals with retardation in the electrostatic interaction between the time-dependent electron density and its environment, here in the context of hybrid schemes coupling RT-TDDFT to polarizable Molecular Mechanics force fields (MMpol). We found that the latter retardation effects can be safely neglected because of the rapid damping vs. distance of the electric fields created by electrostatic dipole moments. This conclusion is also relevant for methodologies, coupling RT-TDDFT to implicit polarizable continuum models. On the other hand, our results recommend the use of the LWP for modelling molecule-ion collisions by first-principles simulations. Remarkably, ionization takes place on faster time scales when relativistic corrections are introduced even for incident kinetic energies of 0.1 MeV.

Given an expression for the quantum mechanical action of an N -electron system as a functional of N time-dependent spin orbitals, we present a method of constructing the variationally best local time-dependent single-particle potentials which, when inserted in time-dependent singleparticle Schrodinger equations for the spin-up and spin-down electrons yield orbitals that make stationary. We also propose a simplification of this scheme leading to a time-dependent generalization of the static optimized effective potentials recently introduced by Krieger, Li, and Iafrate [Phys. Lett. A 146, 256 (1990)]. Owing to rapid experimental progress in the field of laser physics, ultrashort laser pulses of very high intensity have become available in recent years. The electric field produced in such pulses can reach the strength of the electric field caused by atomic nuclei. If an atomic system is placed in the focus of such a laser pulse, one observes a wealth of new phenomena [1] which cannot be explained by perturbation theory. The nonperturbative quantum mechanical description of interacting particles moving in a very strong time-dependent external field therefore has become a prominent problem of theoretical physics. Since its rigorous foundation by Runge and Gross [2], time-dependent density functional theory (TDDFT) [3 ‐ 5] is available as a method to deal with time-dependent many-particle problems of this kind. The central statement of TDDFT is that the time-dependent density of a system of interacting particles moving in an external potential can be calculated, in principle exactly, from a set of time-dependent single-particle equations which can be viewed as the time-dependent counterpart of the Kohn-Sham scheme. These singleparticle equations involve an exchange-correlation potential, , which is a functional of and has to be approximated in practice. An extension of TDDFT to spin-polarized systems has been proposed by Liu and Vosko [6]. Neglecting magnetic effects associated with the orbital motion of the electrons, they consider external time-dependent potentials acting on electrons with spin only. In this case, two different corresponding to the two spin orientations are needed which are functionals of the spin densities . Again, the key problem is to obtain good approximations of . To date, only a rather crude adiabatic approximation is available which adopts the functional form of the static exchangecorrelation potential. The purpose of this paper is to introduce a different approach to the construction of

We study the linear response of pure and doped metal clusters to spin-dependent and spin-independent external fields within the framework of the time-dependent density functional theory. As test cases we have considered the response of clusters with spin-saturated configurations (Na$_{9}^{+}$, Na$_{8}$, Na$_{21}^{+}$, Na$_{20}$, Na$_{40}$, Na$_{4}$Pb and Na$_{6}$Pb) and with spin-polarized configurations (Na$_{6}^{+}$, Na$_{5}$Pb, Al$_{11}$Fe, Al$_{18}$ and Al$_{18}$Fe). For spin-dependent excitations we have obtained in all the pure and doped sodium clusters a strongly collective spin mode of surface type lying at lower energies than the unperturbed particle-hole excitations. This mode uncouples cleanly from the electric dipole mode in the case of spin-saturated clusters, but for spin-polarized clusters these two modes turn out to be intertwined in the responses to spin-dependent and to spin-independent fields. We have performed the calculations within two different exchange-correlation potentials, the first constructed from the local density approximation by Perdew and Wang and the second constructed by Parr and Ghosh starting from the strongly non-local Amaldi Approximation. The latter incorporates the correct -1/r long-range behaviour leading to calculated static polarizabilities and photoabsorption spectra closer to experiments that the results from local density calculations. For the doped clusters Na$_{n}$Pn and Al$_{n}$Fe we have compared the results obtained within two descriptions of the atoms surrounding the central impurity atom, namely the jellium model and the spherical average of the pseudopotentials method. The polarizabilities of Al$_{n}$Fe clusters with n ≤ 18, calculated within the two ionic models are similar and for n > 9 are also similar to those of pure Al$_{n}$ clusters. The main difference between jellium and pseudopotential models when describing doped Al$_{n}$Fe clusters is obtained for the dipole response at several tens of eV for certain sizes where the last occupied d orbital has different occupation number in the pseudopotential model than in the jellium model.