One-particle Description Research Articles

Contactium: A strongly correlated model system.

At the limit of an infinite confinement strength ω, the ground state of a system that comprises two fermions or bosons in harmonic confinement interacting through the Fermi-Huang pseudopotential remains strongly correlated. A detailed analysis of the one-particle description of this "contactium" reveals several peculiarities that are not encountered in conventional model systems (such as the two-electron harmonium atom, ballium, and spherium) involving Coulombic interparticle interactions. First of all, none of the natural orbitals (NOs) {ψn(ω;r)} of the contactium is unoccupied, which implies nonzero collective occupancies for all the angular momenta. Second, the NOs and their non-ascendingly ordered occupation numbers {νn} turn out to be related to the eigenfunctions and eigenvalues of a zero-energy Schrödinger equation with an attractive Gaussian potential. This observation enables the derivation of their properties, such as the n-4/3 asymptotic decay of νn at the n→∞ limit (which differs from that of n-8/3 in the Coulombic systems), the independence of the confinement energy vn=⟨ψn(ω;r)|12ω2r2|ψn(ω;r)⟩ of n, and the n-2/3 asymptotic decay of the respective contribution νntn to the kinetic energy. Upon suitable scaling, the weakly occupied NOs of the contactium turn out to be virtually identical to those of the two-electron harmonium atom at the ω → ∞ limit, despite the entirely different interparticle interactions in these systems.

Multibody expansion of the local integrals of motion: how many pairs of particle-hole do we really need to describe the quasiparticles in the many-body localized phase?

The emergent integrability in a many-body localized (MBL) system can be well characterized by the existence of the complete set of local integrals of motion (LIOMs). Such exactly conserved and exponentially localized operators are often understood as quasiparticle operators which can be expanded in terms of single-particle operators dressed with different numbers of particle-hole pairs. Here, we consider a one-dimensional XXZ spin- Heisenberg chain in the presence of a random field and try to quantify the corrections needed to be considered in the picture of quasiparticles associated with LIOMs due to the presence of particle-hole excitations. To this end, we explicitly present the multibody expansion of LIOM creation operators of the system in the MBL regime. We analytically obtain the coefficients of this expansion and discuss the effect of higher-order corrections associated with different numbers of particle-hole excitations. Our analysis shows that depending on the localization length of the system, there exist a regime in which the contributions that come from higher-order terms can break down the effective one-particle description of the LIOMs and such quasiparticles become essentially many-body-like.

Excited state dynamics in monolayer black phosphorus revisited: Accounting for many-body effects.

The dynamics of electron-hole recombination in pristine and defect-containing monolayer black phosphorus (ML-BP) has been studied computationally by several groups relying on the one-particle description of electronic excited states. Our recent developments enabled a more sophisticated and accurate treatment of excited states dynamics in systems with pronounced excitonic effects, including 2D materials such as ML-BP. In this work, I present a comprehensive characterization of optoelectronic properties and nonadiabatic dynamics of the ground state recovery in pristine and divacancy-containing ML-BP, relying on the linear-response time-dependent density functional theory description of excited states combined with several trajectory surface hopping methodologies and decoherence correction schemes. This work presents a revision and new implementation of the decoherence-induced surface hopping methodology. Several popular algorithms for nonadiabatic dynamics algorithms are assessed. The kinetics of nonradiative relaxation of lower-lying excited states in ML-BP systems is revised considering the new methodological developments. A general mechanism that explains the sensitivity of the nonradiative dynamics to the presence of divacancy defect in ML-BP is proposed. According to this mechanism, the excited states' relaxation may be inhibited by the presence of energetically close higher-energy states if electronic decoherence is present in the system.

Exact path-integral evaluation of locally interacting systems: The subtlety of operator ordering

We discuss how one calculates the coherent path integrals for locally interacting systems, where some inconsistencies with exact results have been reported previously. It is shown that the operator ordering subtlety that is hidden in the local interaction term modifies the Hubbard-Stratonovich transformation in the continuous time formulation, and it helps reproduce known results by the operator method. We also demonstrate that many-body effects in the strong interaction limit can be well characterized by the free-particle theory that is subject to annealed random potentials and dynamical gauge (or phase) fields. The present treatment expands the conventional paradigm of the one-particle description, and it provides a simple, viable picture for strongly correlated materials of either bosonic or fermionic systems.

Quantum Particles from Classical Probabilities in Phase Space

Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow, including interference or tunneling. The appropriate quantum observables for position and momentum contain a statistical part which reflects the roughness of the probability distribution. “Zwitters” realize a continuous interpolation between quantum and classical particles. Such objects may provide for an effective one-particle description of classical or quantum collective states as droplets of a liquid, macromolecules or a Bose-Einstein condensate. They may also be used for quantitative fundamental tests of quantum mechanics. We show that the ground state for zwitters has no longer a sharp energy. This feature permits to put quantitative experimental bounds on a small parameter for possible deviations from quantum mechanics.

Effective bandstructure in the insulating phase versus strong dynamical correlations in metallicVO2

Using a general analytical continuation scheme for cluster dynamical mean-field calculations, we analyze real-frequency self-energies, momentum-resolved spectral functions, and one-particle excitations of the metallic and insulating phases of ${\text{VO}}_{2}$. While for the former dynamical correlations and lifetime effects prevent a description in terms of quasiparticles, the excitations of the latter allow for an effective bandstructure. We construct an orbital dependent, but static one-particle potential that reproduces the essentials of the full many-body spectrum. Yet, the ground state is well beyond a static one-particle description. The emerging picture gives a nontrivial answer to the decade-old question of the nature of the insulator, which we characterize as a ``many-body Peierls'' state, stressing the joint effect of lattice symmetry breaking and Coulomb correlations.

Time-evolution of highly localized positive-energy states of the free Dirac electron

Highly localized positive-energy states of the free Dirac electron are constructed and shown to evolve in a simple way under the action of Dirac's equation. When the initial uncertainty in position is small on the scale of the Compton wavelength, there is an associated uncertainty in the mean energy that is large compared with the rest mass of the electron. However, this does not lead to any breakdown of the one-particle description, associated with the possibility of pair-production, but rather leads to a rapid expansion of the probability density outwards from the point of localization, at speeds close to the speed of light.

Do many-particle neutrino interactions cause a novel coherent effect?

We investigate whether coherent flavor conversion of neutrinos in a neutrino background is substantially modified by many-body effects, with respect to the conventional one-particle effective description. We study the evolution of a system of interacting neutrino plane waves in a box. Using its equivalence to a system of spins, we determine the character of its behavior completely analytically. We find that, if the neutrinos are initially in flavor eigenstates, no coherent flavor conversion is realized, in agreement with the effective one-particle description. This result does not depend on the size of the neutrino wavepackets and therefore has a general character. The validity of the several important applications of the one-particle formalism is thus confirmed.

Theoretical Study of H+Translocation along a Model Proton Wire

The mechanism of proton translocation along linear hydrogen-bonded water chains is investigated. Classical and discretized Feynman path integral molecular dynamics simulations are performed on protonated linear chains of 4, 5, and 9 water molecules. The dissociable and polarizable water model PM6 of Stillinger and co-workers is used to represent the potential energy surface of the systems. The simulations show that quantum and thermal effects are both important because the height of the barriers opposing proton transfer are strongly coupled to the configuration of the chain, which is, in turn, affected by the presence of an excess proton. For characterization of the quantum effects, the energy levels of the hydrogen nucleus located at the center of a protonated tetrameric water chain are calculated by solving the Schroedinger equation for an ensemble of configurations which were generated with path integral simulations. Analysis shows that the first excitation energies are significantly larger than the thermal energy kBT and that quantum effects are dominated by the zero-point energy of the proton. The quantum correlations between the different proton nuclei are found to be negligibly small, suggesting that an effective one-particle description could be valid. Potential of mean force surfaces for proton motion in relation to the donor−acceptor separation are calculated with classical and path integral simulations for tetrameric and pentameric water chains. The mechanism for long-range proton transfer is illustrated with a simulation of a hydrogen-bonded chain of nine water molecules. During the simulation, cooperative fluctuations which modulate the asymmetry of the chain enable the spontaneous translocation of protons over half of the length of the chain.

Ab initio cluster and band structure calculations on systems modeling La 2CuO 4. Effects of charge transfer between the different planes, Madelung potentials, doping and correlations

Based on an initio Hartree-Fock (HF) calculations both on the cluster and aand structure level, the electronic structure of La 2CuO 4 (2-1-4) was investigated. As model systems [CuO 6] n− (cluster case) and [CuO 4] m− units (band structure case) were chosen, i.e. the “apical” oxygens were explicitly included. Surrounding ions were treated as point charges (cluster case) and via partially self-consistent Madelung potentials (band structure case), respectively. Using the HF approximation we found a too low density of states (DOS) around the Fermi level, while the charge distribution in the ground state seems to be reasonable. To obtain DOS curves comparable with the experimental ones, we had to go beyond the one-particle description by using Møller-Plesset many-body perturbation theory. A comparison with density functional (DF) calculations in the local density approximation (LDA) is given. Finally, we studied the effects of doping on the HF level. Here we found that upon doping holes of ω symmetry and predominant oxygen character are formed within the CuO 2 planes of 2-1-4. At the same time increasing covalent bonding between in-plane Cu and O was observed.

Full Potential Electronic Structure Calculations and the Concept of Stress Fields and Energy Densities for Total Energy Calculations

ABSTRACTWith the availability of reliable full atomic cell orbitals the possibility arises to calculate pressure or stress, restoring or relaxation driving Hellmann -Feynman forces, and total energies (especially of defects) alternatively and directly via stress tensor fields and energy densities, two local quantities. Although quantum mechanical stress field and energy density can not be defined uniquely, there is a recent interest in these quantities, because integrals with physical meaning are gauge invariant.The mentioned fields can be defined (i) for the full many-body description with the exact one-particle density matrix and pair distribution function as well as (ii) for the Kohn-Sham one-particle description with LDA or beyond (gradient expansion approximation). If the local stress field for a special system once is constructed, then the global stress tensor and /or forces on nuclei can be calculated via the stress theorem and the force theorem by means of unit cell surface integrals. The energy density can be derived from the terms of the stress field by taking the trace and can be used to calculate defect energies without bothering about the thermodynamic limit.

A TWO-BAND SUPERCONDUCTOR WITH A NARROW BAND NEAR THE FERMI LEVEL

The modern theory of conventional superconductivity is based upon the concept of quantum states with broken gauge symmetry providing non-zero values for the so-called "anomalous averages" [Formula: see text], [Formula: see text]. Being applied to the simplest Gorikov-like semiphenomenological electronic scenario for a metal superconductor, this idea (in the mean field approximation) leads towards a complete description of all properties of ordinary superconductors as a manifestation of macroscopic quantum phase coherence. Currently there exists already strong experimental evidence that the newly discovered high Tc superconductors exhibit the same quantum coherence effects including the highly characteristic quantity for these phenomena, namely the doubled electronic charge. On these grounds one can expect that the high Tc superconductors should also be described by "anomalous averages" of the same kind. The only question is whether Gorikov's scenario is still sufficient or we need a new scenario instead in order to grasp the whole situation. In the case of Gorikov's scenario one needs to explain how the strong electron-electron coupling (no matter of what origin) can be consistent with the system stability condition. Yet there is another argument in favour of a new scenario. The large variety of the new SC properties cannot be explained by a model with too limited number of physical parameters. In our dealing with the problem of a possible new scenario we have suggested that in order to understand the high T c superconductors one should not perhaps go so far as to doubt the one-particle approximation and to introduce the Hubbard-like models, RVB and so on. Taking into account the crystalline structure of perfect high T c superconductors we have assumed within the one-particle description the two overlapping bands approach which was proposed by Suhl, Mattias and Walker (USA) and Moskalenko (USSR) as early as in 1959. To obtain qualitatively new results we have suggested a sharp asymmetry between the two bands (one being practically a local energy level close to the Fermi level) and also a special structure of direct electron-electron interaction with dominating interband scattering of singlet electron pairs described by an amplitude g. As the final analysis has shown, an inevitable but comparatively small splitting of the two bands does not invalidate the results of the model. As to the peculiar structure of interaction we believe it might be explained through a strong electron-optical phonon coupling due to the Jahn-Teller-like instability manifested in tetragonal-orthorhombic transitions of HT c samples. The model just outlined can indeed yield high T c . In the mean field approximation (with two superconductivity order parameters) the order of magnitude of T c is given by T c ~ (|g|N(o)/2)2 EF where N(o) is the density of states in the wide band at the Fermi level and EF is a wide band width. There is an exponentially sharp decline of T c while overdoping or underdoping the system and there is also a broad plateau when the narrow band is filled partially (the heavy fermion situation). The other results of calculations including thermodynamics and also kinetic properties for the normal state do not contradict experiments except for the linear temperature dependence of the specific heat observed sometimes. But one must take into account that in reality all high T c superconductors are in fact disordered solutions, and it is necessary to consider the dirty alloy limit with Anderson's theorem being violated because of the narrow band existence. At the same time, as analysis shows, the mean field approximation is not good enough for the model (the small parameter is only ( log 2/|g|N(o))-1) and therefore one has to apply Green's functions technique in order to correct the results. There is also a possibility that the magnetic properties connected with localized spins (if there are any) must be taken into account as well.

Numerical solution of the relativistic pair equation.

Correlation has been treated relativistically by solutions of the pair equation, an inhomogeneous differential equation in two dimensions. The equation is solved within the no--(virtual-)pair approximation and is formally correct to order ${\ensuremath{\alpha}}^{2}$ Ry. Continuum dissolution is rigorously avoided, by the use of projection operators. Correlation is treated starting from a suitable choice of a fully relativistic one-particle description of the atom. The solution of the equation involves additional difficulties as compared with the nonrelativistic case, which are discussed. Second-order energies arising from electrostatic and magnetic correlation have been calculated for the 1${s}^{2}$ ground state for a series of heliumlike systems (Z=2--50). The starting point has been either hydrogenlike wave functions or Dirac-Fock orbitals. Comparison has been made with other methods, showing good, sometimes excellent, agreement, and trends in the isoelectronic series are discussed. By iterative solutions of the exact pair equation a nonperturbative treatment of the two-body part of the static Coulomb interaction is obtained. This procedure has been used for s excitations.

Valence photoionization of hydrogen fluoride with synchrotron radiation

Photoionization from hydrogen fluoride has been studied with synchrotron radiation in the 30–130 eV photon energy range. Relative photoelectric cross sections have been obtained for the 1π (ionization energy of 16.1 eV) MO, the 3σ MO (19.9 eV ionization energy), and in some cases the inner 2σ valence MO (I.E.=39.6 eV). Comparison is made with other measurements such as quasiphotoionization results and with one-center calculations. Angular distribution asymmetry parameters have also been measured for the 1π and 3σ MO’s and compared with those of Ne2p. In the inner valence region, satellites have been observed; this is in accord with most theoretical calculations which predict the breakdown of the one-particle description in this region.

Correlation in a relativistic framework

By the use of projection operators, defined in Dirac space, it is shown how a relativistic pair equation, correct to order α 2Ry, can be constructed. It is pointed out how the Brown-Ravenhall disease (continuum dissolution) is rigorously avoided with this procedure. The pair equation treats correlation relativistically starting from a suitable choice of a fully relativistic one-particle description of the atom. Second order contributions to the energy from the electrostatic correlation have been calculated for the 1s 2 ground state of some two-body systems. The starting point has been either hydrogen-like wave functions ( Z = 2, 10) or Dirac-Fock orbitals ( Z 10−60). Excitations to s 2, p 2, d 2 and f 2 have been treated and an unexpected behaviour of the p 2 1 2 excita P 2 3 2 one is discussed. By iterative solutions of the exact pair equation a nonperturbative treatment of the two-body part of the s Coulomb interaction is obtained. This procedure has been used for s excitations ( Z = 2−20) and a comparison of the relativistic and nonrelativistic behaviour is made.

Generalized Kohn-Sham theory for electronic excitations in realistic systems.

Instead of expressing the total energy of an interacting electron system as a functional of the one-particle density as in the Hohenberg-Kohn-Sham theory, we use a conventional approach in determining total energies by forming the expectation value 〈scrH〉 of the N-electron Hamiltonian with the true wave function \ensuremath{\Psi}${(\mathrm{q}}_{1}$,${\mathrm{q}}_{2}$,...,${\mathrm{q}}_{N}$). We introduce a new concept of partitioning \ensuremath{\Psi}${(\mathrm{q}}_{1}$,${\mathrm{q}}_{2}$,...,${\mathrm{q}}_{N}$) into two components such that the one-particle density is connected with the first component only. If one requires 〈scrH〉 to be stationary against variation of \ensuremath{\Psi}${(\mathrm{q}}_{1}$,${\mathrm{q}}_{2}$,...,${\mathrm{q}}_{N}$) , this first component turns out to be one Slater determinant in terms of one-particle states which obey Kohn-Sham--type one-particle equations. Hence, the expression for the one-particle density becomes identical to that of the Kohn-Sham theory. The virtues of the new approach, particularly its capability of describing thermal excitation in solids, optical transitions, etc., are discussed in detail. We also address the so-called gap problem which has recently been an extensively debated subject within the one-particle description of N-electron systems.

Breakdown in the Koopmans' theorem interpretation of the outer valence-level photoemission spectra of selected organic molecules

Various final-state manifestations arising from a breakdown in a Koopmans' theorem interpretation of the lower-lying valence level photoemission spectra of benzene, p-quinodimethane, trans-butadiene, p-nitroaniline, trans-stilbene and acrolein are addressed within the semi-empirical open-shell RHF CNDO/S(CI) approximation. The results on benzene, trans-butadiene and p-quinodimethane support previous interpretations based on experimental and/or theoretical arguments of pronounced many-body interactions for ionizations between 9 and 14 eV. Computations on p-nitroaniline indicate an unusually strong breakdown in the one-particle description of photoionization at = 10.0 eV due to coupling between appropriate primary hole-states and concomitant one-electron excitations to low-lying virtual levels having considerable localization on the nitro group. The open-shell RHF CNDO/S(CI) energy and projected hole-state distributions yield theoretical photoemission spectra for the molecules considered which offer considerable improvement over the Koopmans' theorem assignment.

Ground States, Configurations, and Truncated Orbital Bases of the Iron-Series Atoms

This article presents an analysis of several related topics of importance to the orbital theory of electronic states of transition-metal atoms in the framework of the Hartree–Fock approximation. First, it is shown that the principle experimental features of the term separations for these atoms are determined primarily by the Hartree–Fock wavefunction. Within the framework of this one-particle description, it is then demonstrated that subtle competing electrostatic effects are responsible for the well-known inversions of ground-state configurations. Beyond the one-particle description, electron correlation contributions, determined as differences between experimental and Hartree–Fock term separations, are demonstrated to have remarkably systematic trends that enable predictions to be made of term values of stable but unobserved excited states of the ions. Finally, useful small bases that maintain the principal features of the Hartree–Fock description for reliable exploratory SCF calculations on these atoms and their molecules are presented and discussed.