Energy convexity as a consequence of decoherence and pair-extensive interactions in many-electron systems
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nuclear (including radiation effects), defects, me↗
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Transition from nonsequential to sequential double ionization in many-electron systems
Understanding strong-field double ionization of many-electron systems is an important fundamental problem with potential implications for molecular imaging within this regime. Using mid-IR radiation, we unambiguously identify the transition from nonsequential (e, 2e) to sequential double ionization in Xe at an intensity below 10 14 W/cm 2 . Ionization from excited orbitals is found to be decisive at low intensities, but we demonstrate that such mechanisms are unimportant in the sequential regime. We utilize these facts to successfully image a molecular dication using laser-induced electron diffraction. This methodology can be used to study molecular dynamics on unprecedented few-femtosecond time scales.
74 ATOMIC AND MOLECULAR PHYSICS↗
Revealing the dynamics of ultrarelativistic non-equilibrium many-electron systems with phase space tomography
The description of physical processes with many-particle systems is a key approach to the modeling of numerous physical systems. For example in storage rings, where ultrarelativistic particles are agglomerated in dense bunches, the modeling and measurement of their phase-space distribution is of paramount importance: at any time the phase-space distribution not only determines the complete space-time evolution but also provides fundamental performance characteristics for storage ring operation. Here, we demonstrate a non-destructive tomographic imaging technique for the 2D longitudinal phase-space distribution of ultrarelativistic electron bunches. For this purpose, we utilize a unique setup, which streams turn-by-turn near-field measurements of bunch profiles at MHz repetition rates. To demonstrate the feasibility of our method, we induce a non-equilibrium state and show that the phase-space distribution microstructuring as well as the phase-space distribution dynamics can be observed in great detail. Our approach offers a pathway to control ultrashort bunches and supports, as one example, the development of compact accelerators with low energy footprints.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Dynamical vertex approximation for many-electron systems with spontaneously broken SU(2) symmetry
We generalize the formalism of the dynamical vertex approximation (DΓA)—a diagrammatic extension of the dynamical mean-field theory (DMFT)—to treat magnetically ordered phases. To this aim, we start by concisely illustrating the many-electron formalism for performing ladder resummations of Feynman diagrams in systems with broken SU(2) symmetry associated to ferromagnetic (FM) or antiferromagnetic (AF) order. We then analyze the algorithmic simplifications introduced by taking the local approximation of the two-particle irreducible vertex functions in the Bethe-Salpeter equations, which defines the ladder implementation of DΓA for magnetic systems. The relation of this assumption with the DMFT limit of large coordination-number/high dimensions is explicitly discussed. As a last step, we derive the expression for the ladder DΓA self-energy in the FM- and AF-ordered phases of the Hubbard model. The physics emerging in the AF-ordered case is explicitly illustrated by means of approximated calculations based on a static mean-field input for DΓA equations. The results obtained capture fundamental aspects of both metallic and insulating ground states of two-dimensional antiferromagnets, providing a reliable compass for future, more extensive applications of our approach. Furthermore, possible routes to further develop diagrammatic-based treatments of magnetic phases in correlated electron systems are briefly outlined in the Conclusions.
2-dimensional systems↗
Many-Electron System on Helium and Color Center Spectroscopy
Electrons on the helium surface display sharp resonant absorption lines related to the transitions between the subbands of quantized motion transverse to the surface. A magnetic field parallel to the surface strongly affects the absorption spectrum.We show that the effect results from admixing the intersubband transitions to the in-plane quantum dynamics of the strongly correlated electron liquid or a Wigner crystal. This is similar to the admixing of electron transitions in color centers to phonons. Furthermore, the spectrum permits a direct characterization of the many-electron dynamics and also enables testing the theory of color centers in a system with controllable coupling.
36 MATERIALS SCIENCE↗
Temperature-dependent behavior of confined many-electron systems in the Hartree-Fock approximation
Not Available
Sjostrom, Travis↗
The dissociation energy of Cu2 - Do we want to perform multi-reference singles and doubles CIs on many-electron systems?
Reference is made to a study by Hay and Dunning (1976), who showed that, for most problems, it is not necessary to perform full FOCI (first order configuration interaction); instead, only that subset of configuration state functions (CSFs) that differ by only one or two spin orbitals from any of a list of reference configurations need be used. This is referred to as POLCI. Calculations of the D(e) of Cu2 using both SDCI (singles and doubles configuration interaction) and POLCI models are presented. It is found that the size-consistency problems associated with SDCI cause an error in D(e), whereas the POLCI results are in excellent agreement with experiment. It is proposed that the orbitals be classified as inactive and active and that the inactive-inactive correlation be eliminated to reduce the size-consistency error. In addition, it is recommended that SDCI treatments be applied with caution to systems having a large number of electrons.
Bauschlicher, C. W., Jr.↗
A theory for colors of strongly correlated electronic systems
Many strongly correlated transition metal insulators are colored, even though they have band gaps much larger than the highest energy photons from the visible light. An adequate explanation for the color requires a theoretical approach able to compute subgap excitons in periodic crystals, reliably and without free parameters—a formidable challenge. The literature often fails to disentangle two important factors: what makes excitons form and what makes them optically bright. We pick two archetypal cases as examples: NiO with green color and MnF 2 with pink color, and employ two kinds of ab initio many body Green’s function theories; the first, a perturbative theory based on low-order extensions of the $GW$ approximation, is able to explain the color in NiO, while the same theory is unable to explain why MnF 2 is pink. We show its color originates from higher order spin-flip transitions that modify the optical response, which is contained in dynamical mean-field theory (DMFT). We show that symmetry lowering mechanisms may determine how ‘bright’ these excitons are, but they are not fundamental to their existence.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Exact differential equation for the density and ionization energy of a many-particle system
The present investigation is concerned with relations studied by Hohenberg and Kohn (1964) and Kohn and Sham (1965). The properties of a ground-state many-electron system are determined by the electron density. The correct differential equation for the density, as dictated by density-functional theory, is presented. It is found that the ground-state density n of a many-electron system obeys a Schroedinger-like differential equation which may be solved by standard Kohn-Sham programs. Results are connected to the traditional exact Kohn-Sham theory. It is pointed out that the results of the current investigations are readily extended to spin-density functional theory.
Levy, M.↗
Limitations of the semirelativistic approach in sum rules and related calculations in atomic physics
The semirelativistic approach, as applied to sum-rule calculations, can yield very inaccurate results for high-Z systems; the apparently good agreement previously reported is fortuitous, due to the application of an approximate eigenstate of the semirelativistic Hamiltonian. Attention is given to one-electron atomic systems, and the results obtained are discussed with a view to their implications for many-electron systems. The many-electron problem is complicated by a lack of clarity as to the relative importance of contributions due to correlation effects among the electrons, their effect on the E2 oscillator strength, and the retardation correction to the E1 transition.
Rustgi, M. L.↗
Stretched or noded orbital densities and self-interaction correction in density functional theory
Semilocal approximations to the density functional for the exchange-correlation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semilocal approximation makes that approximation exact for all one-electron ground- or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semilocal approximations satisfy, suggesting the need for a generalized SIC. These conclusions are supported by calculations for one-electron densities and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGAs) and meta-GGAs, it reduces and often worsens the atomization energies of molecules. Thus, PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here, in particular, to the strongly constrained and appropriately normed (SCAN) meta-GGA, for which the correlation part is already self-interaction-free. This property makes SCAN a natural first candidate for a generalized SIC.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Real-Space Multiple-Scattering Theory and Its Applications at Exascale
In recent decades, the ab initio methods based on density functional theory (DFT) (Hohenberg and Kohn 1964, Kohn and Sham 1965) have become a widely used tool in computational materials science, which allows theoretical prediction of physical properties of materials from the first principles and theoretical interpretation of new physical phenomena found in experiments. In the framework of DFT, the original problem that requires solving a quantum mechanical equation for a many-electron system is reduced to a one-electron problem that involves an electron moving in an effective field, while the effective field potential is made up of an electrostatic potential, also known as Hartree potential, arising from the electronic and ion charge distribution in space and an exchange–correlation potential, which is a function of the electron density and encapsulates the exchange and correlation effects of the many-electron system. Even though the exact functional form of the exchange-correlation potential is formally unknown, a local density approximation (LDA) or a generalized gradient approximation (GGA) is usually applied so that the calculation of the exchange–correlation potential, as well as the exchange–correlation energy, becomes tractable while a required accuracy is retained. Based on DFT, ab initio electronic structure calculations for a material generally involve a self-consistent process that iterates between two computational tasks: (1) solving an one-electron Schrödinger equation, also known as Kohn–Sham equation, to obtain the electron density and, if needed, the magnetic moment density, and (2) solving the Poisson equation to obtain the electrostatic potential corresponding to the electron density and constructing the effective potential by adding the exchange–correlation potential to the electrostatic potential. This self-consistent process proceeds until a convergence criteria is reached.
Eisenbach, Markus↗
Characterization of multielectron dynamics in molecules: A multiconfiguration time-dependent Hartree-Fock picture
Using the framework of multiconfiguration theory, where the wavefunction Φ(t) of a many-electron system at time t is expanded as Φ(t)=∑{sub I}C{sub I}(t)Φ{sub I}(t) in terms of electron configurations (Φ{sub I}(t)), we divided the total electronic energy E(t) as E(t)=∑{sub I}|C{sub I}(t)|{sup 2}E{sub I}(t) . Here E{sub I}(t) is the instantaneous phase changes of C{sub I}(t) regarded as a configurational energy associated with Φ{sub I}(t). We then newly defined two types of time-dependent states: (i) a state at which the rates of population transfer among configurations are all zero; (ii) a state at which (E{sub I}(t)) associated with the quantum phases of C{sub I}(t) are all the same. We call the former time-dependent state a classical stationary state by analogy with the stationary (steady) states of classical reaction rate equations and the latter one a quantum stationary state. The conditions (i) and (ii) are satisfied simultaneously for the conventional stationary state in quantum mechanics. We numerically found for a LiH molecule interacting with a near-infrared (IR) field ε(t) that the condition (i) is satisfied whenever the average velocity of electrons is zero and the condition (ii) is satisfied whenever the average acceleration is zero. We also derived the chemical potentials μ{sub j}(t) for time-dependent natural orbitals ϕ{sub j}(t) of a many-electron system. The analysis of the electron dynamics of LiH indicated that the temporal change in Δμ{sub j}(t) ≡ μ{sub j}(t) + ε(t) · d{sub j}(t) − μ{sub j}(0) correlates with the motion of the dipole moment of ϕ{sub j}(t), d{sub j}(t). The values Δμ{sub j}(t) are much larger than the energy ζ{sub j}(t) directly supplied to ϕ{sub j}(t) by the field, suggesting that valence electrons exchange energy with inner shell electrons. For H{sub 2} in an intense near-IR field, the ionization efficiency of ϕ{sub j}(t) is correlated with Δμ{sub j}(t). Comparing Δμ{sub j}(t) to ζ{sub j}(t), we found that energy accepting orbitals of Δμ{sub j}(t) > ζ{sub j}(t) indicate high ionization efficiency. The difference between Δμ{sub j}(t) and ζ{sub j}(t) is significantly affected by electron-electron interactions in real time.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Role of polarization interaction in photoionization of negative ions of alkali metals
Photoionization processes of negative ions of sodium, potassium, and rubidium were investigated. Calculations of the dependence of the photoionization cross section on the photon energy were performed within the Random Phase Approximation with Exchange for outer subshells (RPAE) and within the Generalized Random Phase Approximation with Exchange (GRPAE) for inner subshells. The latter theoretical approach includes both many-electron correlations and core rearrangement due to escape of one of the electrons from the system. The results of calculations for the negative sodium ion were found to be in good agreement with experimental data. Better agreement was achieved by allowing dynamical polarization of the electron core. It manifests itself as a many-electron response to variation of the external electromagnetic field, which results from the excitation of the many-electron system. Detailed study of the main mechanisms determining the cross section dependence profile was carried out. These mechanisms are the inter- and intrachannel correlations acting as a many-electron response to the external field, the electron core rearrangement, and the dynamic polarization. Besides sodium and potassium ions, photoionization of rubidium ion was investigated. A new method accounting for polarization corrections to optical transition amplitudes based on combination of the Dyson equation and RPAE is proposed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Perdew-Zunger self-interaction correction: How wrong for uniform densities and large- Z atoms?
Semilocal density functionals for the exchange-correlation energy of a many-electron system cannot be exact for all one-electron densities. In 1981, Perdew and Zunger (PZ) subtracted the fully nonlocal self-interaction error orbital-by-orbital, making the corrected functional exact for all collections of separated one-electron densities and making no correction to the exact functional. Although the PZ self-interaction correction (SIC) eliminates many errors of semilocal functionals, it is often worse for equilibrium properties of sp-bonded molecules and solids. Nonempirical semilocal functionals are usually designed to be exact for electron gases of uniform density and, thus, also make 0% error for neutral atoms in the limit of large atomic number Z, but PZ SIC is not so designed. For localized SIC orbitals, we show analytically that the local spin density approximation (LSDA)-SIC correlation energy per electron of the uniform gas in the high-density limit makes an error of -50% in the spin-unpolarized case and -100% in the fully spin-polarized case. Then we extrapolate from the Ne, Ar, Kr, and Xe atoms to estimate the relative errors of the PZ SIC exchange-correlation energies (with localized SIC orbitals) in the limit of large atomic number: about +5.5% for the LSDA-SIC and about -3.5% for nonempirical generalized gradient [Perdew-Burke-Ernzerhof (PBE)-SIC] and meta-generalized gradient strongly constrained and appropriately normed (SCAN)-SIC approximations. Finally, the SIC errors are considerably larger than those that have been estimated for LSDA-SIC by approximating the localized SIC orbitals for the uniform gas and may explain the errors of PZ SIC for equilibrium properties, opening the door to a generalized SIC that is more widely accurate.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Machine learning predictions for local electronic properties of disordered correlated electron systems
We present a scalable machine learning (ML) model to predict local electronic properties such as on-site electron number and double occupation for disordered correlated electron systems. Our approach is based on the locality principle, or the nearsightedness nature, of many-electron systems, which means local electronic properties depend mainly on the immediate environment. A ML model is developed to encode this complex dependence of local quantities on the neighborhood. We demonstrate our approach using the square-lattice Anderson-Hubbard model, which is a paradigmatic system for studying the interplay between Mott transition and Anderson localization. We develop a lattice descriptor based on the group-theoretical method to represent the on-site random potentials within a finite region. The resultant feature variables are used as input to a multilayer fully connected neural network, which is trained from data sets of variational Monte Carlo (VMC) simulations on small systems. We show that the ML predictions agree reasonably well with the VMC data. Our work underscores the promising potential of ML methods for multiscale modeling of correlated electron systems.
36 MATERIALS SCIENCE↗
Correlated Dirac–Coulomb–Breit multiconfigurational self-consistent-field methods
The fully correlated frequency-independent Dirac–Coulomb–Breit Hamiltonian provides the most accurate description of electron–electron interaction before going to a genuine relativistic quantum electrodynamics theory of many-electron systems. In this work, we introduce a correlated Dirac–Coulomb–Breit multiconfigurational self-consistent-field method within the frameworks of complete active space and density matrix renormalization group. In this approach, the Dirac–Coulomb–Breit Hamiltonian is included variationally in both the mean-field and correlated electron treatment. Here, we also analyze the importance of the Breit operator in electron correlation and the rotation between the positive- and negative-orbital space in the no-virtual-pair approximation. Atomic fine-structure splittings and lanthanide contraction in diatomic fluorides are used as benchmark studies to understand the contribution from the Breit correlation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗