Nonlocal Correlation Effects Research Articles

Random-Mass Dirac Fermions in an Imaginary Vector Potential: Delocalization Transition and Localization Length

In this and subsequent papers, one dimensional system of Dirac fermions with a random-varying mass is studied by the transfer-matrix methods which we developed recently. We investigate the effects of nonlocal correlation of the spatial-varying Dirac mass on the delocalization transition. Especially we numerically calculate both the "typical" and "mean" localization lengths as a function of energy and the correlation length of the random mass. To this end we introduce an imaginary vector potential as suggested by Hatano and Nelson and solve the eigenvalue problem. Numerical calculations are in good agreement with the results of the analytical calculations. We obtain the relation between the localization length of states and the correlation length of the random mass. In subsequent paper, we shall study Dirac fermions with a random mass of long-ranged correlations.

Effect of non-local correlations in the periodic Anderson model studied by the dynamical cluster approximation

The single particle excitation spectrum of the periodic Anderson model for the half filling case in two dimensions is calculated by using the dynamical cluster approximation (DCA). The DCA method restores the short-ranged inter-site correlations which are neglected in the dynamical mean field approximation (DMFA). A comparison between the results by DCA and DMFA shows that the resonance peak in low energies is suppressed due to the non-local correlations.

What correlation effects are covered by density functional theory?

The electron density distribution ρ(r) generated by a DFT calculation was systematically studied by comparison with a series of reference densities obtained by wavefunction theory (WFT) methods that cover typical electron correlation effects. As a sensitive indicator for correlation effects the dipole moment of the CO molecule was used. The analysis reveals that typical LDA and GGA exchange functional already simulate effects that are actually reminiscent of pair and three-electron correlation effects covered by MP2, MP4, and CCSD(T) in WFT. Correlation functionals contract the density towards the bond and the valence region thus taking negative charge out of the van der Waals region. It is shown that these improvements are relevant for the description of van der Waals interactions. Similar to certain correlated single-determinant WFT methods, BLYP and other GGA functionals underestimate ionic terms needed for a correct description of polar bonds. This is compensated for in hybrid functionals by mixing in HF exchange. The balanced mixing of local and non-local exchange and correlation effects leads to the correct description of polar bonds as in the B3LYP description of the CO molecule. The density obtained with B3LYP is closer to CCSD and CCSD(T) than to MP2 or MP4, which indicates that the B3LYP hybrid functional mimics those pair and three-electron correlation effects, which in WFT are only covered by coupled cluster methods.

Non-local effects in the fermion dynamical mean-field framework; application to the two-dimensional Falicov-Kimball model

We propose a new, controlled approximation scheme that explicitly includes the effects of non-local correlations on the D = solution. In contrast to the usual D = case, the self-energy is self-consistently coupled to two-particle correlation functions. The formalism is general, and is applied to the two-dimensional Falicov-Kimball model. Our approach possesses all the strengths of the large-D solution, and allows one to undertake a systematic study of the effects of inclusion of k-dependent effects on the D = picture. Results for the density of states (), and the single-particle spectral density for the 2D Falicov-Kimball model always yield positive definite (), and the spectral function shows striking new features inaccessible for D = . Our results are in good agreement with the exact results known from the 2D Falicov-Kimball model.

Elastic scattering of photons

Abstract Photon scattering from bound electrons of atoms, a component of the elastic photon-atom scattering amplitude called Rayleigh scattering, is discussed. General features of the many-body scattering amplitude and its partitioning into Rayleigh and Delbruck (and nuclear) single-electron transition scattering amplitudes are examined. The use of the state-of-the-art precise second-order S-matrix calculations of Rayleigh scattering in terms of single-electron transition-amplitudes has led to significant progress in our understanding of the scattering process. The importance of relativistic, higher multipole, and bound-bound contributions in calculating anomalous scattering factor deviations from form factor amplitudes must be emphasized. Accurate interpolation of cross sections in the three-dimensional space of scattering angle, photon energy, and atomic number, utilizing the available published S-matrix data, has permitted extensive tabulation of differential scattering cross sections. S-matrix results may be compared with experiments to assess their validity; they may be compared with simpler but more approximate approaches, to identify the extent of the utility of such approaches and to develop simpler prescription schemes which can give results comparable to the S-matrix results. In spite of their many successes, the present second order S-matrix methods also have limitations and shortcomings, observed in certain recent experiments. We describe the explanation of these experiments in terms of a composite theory which also incorporates non-local exchange and correlation effects. We end with a discussion of other future issues.

Non-locally correlated disorder and delocalization in one dimension (I): Density of states

We study delocalization transition in a one-dimensional electron system with quenched disorder by using supersymmetric (SUSY) methods. Especially we focus on effects of non-local correlation of disorder, for most of studies given so far considered δ-function type white noise disorder. We obtain wave function of the “lowest-energy” state which dominates partition function in the limit of large system size. Density of states is calculated in the scaling region. The result shows that delocalization transition is stable against non-local short-ranged correlation of disorder. Especially states near the band center are enhanced by the correlation of disorder which partially suppresses random fluctuation of disorder. Physical picture of the localization and the delocalization transition is discussed.

Nonlocal electron-positron correlations in solids within the weighted density approximation

Nonlocal electron-positron correlation effects in solids are studied. The weighted density approximation (WDA) is applied to calculations of the nonlocal state-selective electron-positron correlation functions. The importance of state selectivity of the electron-positron enhancement factors is discussed. The calculated WDA electron-positron enhancement factors for the core electrons are compared with those obtained within the local-density approximation. Also, differences in the electron-positron enhancement factors due to the $s,$ $p,$ $d,$ and $f$ angular momentum channels of the electron charge density are studied. The influence of the electron-positron interaction on the positron density distribution in solids is discussed. The formalism is applied to ab initio calculations of positron lifetimes in a variety of metals and silicon. The influence of various approximations to the electron-positron interaction on the positron lifetimes is also presented. Moreover, we study how the core electrons as well as different angular momentum channels of the valence electron density contribute to the total positron annihilation rates and lifetimes. The results are compared to those calculated within the local-density approximation and the generalized gradient approximation.

Manifestations of Nonlocal Exchange, Correlation, and Dynamic Effects in X-Ray Scattering

We report precise measurements of differential x-ray scattering cross sections in Ne and He from 11{endash}22thinspthinspkeV and develop a method for obtaining predictions of comparable accuracy (1{percent} ). The measurement of ratios (total scattering in Ne to He and Compton to Rayleigh scattering in Ne) facilitates comparison to theories. We find evidence for the need to include nonlocal exchange, electron correlation, and dynamic effects for an accurate description at low Z and conclude that no single current theory is sufficient. {copyright} {ital 1998} {ital The American Physical Society }

Quantum computation, entanglement and state reduction

Some general foundational issues of quantum mechanics are considered and are related to aspects of quantum computation. The importance of quantum entanglement and quantum information is discussed a...

On the theory of concentrated hard-sphere suspensions

A systematic theory for the dynamics of hard-sphere suspensions of interacting Brownian particles with both hydrodynamic and direct interactions is presented. A generalized diffusion equation is derived for concentrated suspensions. The volume fraction (φ) dependence of the short- and long-time self-diffusion coefficients are thus explored from a unifying point of view. The long-range hydrodynamic interactions due to the Oseen tensor are shown to play a crucial role in both coefficients, while the short-range hydrodynamic interactions just lead to corrections. The importance of the correlation effects between particles due to the long-range hydrodynamic interactions is also stressed. The nonlocal correlation effect is an important factor, leading to the behavior of the long-time self-diffusion coefficient ( D S L) as D S L ∼ (1 − φ/ φ 0) 2 near the volume fraction of φ 0 = 0.5718. The direct interactions are also found to be drastically reduced by the short-range hydrodynamic interactions.

Calculation of the electron momentum density and Compton scattering measurements for nickel

The (100), (110) and (111) directional Compton profiles of single crystals of nickel have been measured using 59.54 keV 241Am gamma -rays at a 170 degrees scattering angle and a well defined scattering vector. The electron momentum distribution and Compton profiles in nickel have also been calculated on the basis of a self-consistent augmented-plane-wave method within the local-density approximation including a correlation correction term. A quantitative comparison between experimental and theoretical directional Compton profiles shows good agreement and reveals some accurate information about the Fermi surface. Excitations due to nonlocal correlation effects from contributing parts to noncontributing parts of the energy bands are very clearly seen along the (100), (110) and (111) directions. The calculation also reproduces quite well the main features of the observed anisotropies, typically within the experimental error margins, although it slightly overestimates their magnitude.

Apparent barrier height for tunneling electrons in STM

An analysis of the apparent barrier height at a metal-vacuum-metal interface, as a function of separation, is presented for different model potentials. A parametrized model, consistent with recent theoretical work on the barrier potential which takes into account both non-local and local exchange and correlation effects is studied in detail.

Apparent barrier height for tunneling electrons in STM

Abstract An analysis of the apparent barrier height at a metal-vacuum-metal interface, as a function of separation, is presented for different model potentials. A parametrized model, consistent with recent theoretical work on the barrier potential which takes into account both non-local and local exchange and correlation effects is studied in detail.

Electron correlation effect in the momentum density of copper metal.

The total Compton profile for the 〈110〉 direction of crystalline copper has been measured with high statistical accuracy by a \ensuremath{\gamma}-ray scattering experiment. Special attention was paid to the correction of multiple photon scattering in the sample and the slight spectral contamination of the incident \ensuremath{\gamma} radiation. The results are discussed in conjunction with earlier measurements of the Compton profile anisotropies and existing band-structure calculations. The effect of the electron correlation on the Compton profile and the momentum density is found to be significantly larger than in the homogeneous electron gas. A correlation correction functional required by the Hohenberg-Kohn-Sham density-functional theory is calculated in the local density approximation and is shown to improve the agreement between density-functional band-structure calculations and experiment. The remaining discrepancies can be characterized by a redistribution of momentum density in reciprocal space as compared to the model of noninteracting electrons. The appearance of this nonlocal correlation effect is specific for the momentum density and does not contradict the generally good agreement between one-electron theory and other experimental results for copper. Possible origins of the effect are discussed tentatively.

De Haas-van Alphen effect in alkali metal dispersions and the Fermi surface of lithium

Measurements of the de Haas-van Alphen effect in polycrystalline dispersions of metallic lithium are described. X-ray studies indicate that the low-temperature martensitic transformation is suppressed in samples of this form, and that the room temperature BCC structure is retained down to liquid helium temperatures. The de Haas-van Alphen amplitude shows a characteristic beat structure arising from the Fermi surface anisotropy. The radial distortion of the BCC Fermi surface is estimated to be 2.6+or-0.9%. The method of analysis is verified by similar measurements in dispersion of sodium. The results for lithium are consistent with the most recent positron annihilation, Compton scattering and optical absorption data, but yield a Fermi surface distortion which is significantly less than that given by typical bandstructure calculations. This discrepancy lends support to the suggestion of Rasolt, Nickerson and Vosko that non-local exchange and correlation effects may cause a substantial reduction of the Fermi surface anisotropy (see Solid State Commun., vol.16, p.827 (1975)).

Non-local exchange and correlation effects on the fermi surface of lithium

The Fermi surface of lithium was calculated using a non-local exchange and correlation self-energy operator constructed in accord with the density functional formalism. The resulting Fermi surface distortions were found to be drastically reduced from local calculations and in essential agreement with the recent de Haas-van Alphen measurements.

Investigations of nonlocal exchange and correlation effects in metals via the density-functional formalism

The density-functional formalism of Hohenberg, Kohn, and Sham is used to investigate the effects of nonlocal exchange and correlation on the Fermi surface of a simple-cubic metal. The "nonlocal" Fermi surface is obtained by solving the Dyson equation for the quasiparticle states on the Fermi surface with the nonlocal self-energy approximated according to the density-functional scheme in the presence of an external model pseudopotential. This was done by using the corresponding local theory to define a zeroth-order Hamiltonian which provides basis functions to solve the nonlocal eigenvalue problem. It was found that the maximum Fermi-surface distortions obtained from the nonlocal theory were substantially reduced from the local theory, as experiments suggest. The calculations were carried out in the random-phase approximation.

Nonlocal Exchange and Correlation Effects on the Fermi Surface of Metals

The inhomogeneous-electron-gas theory of Hohenberg, Kohn, and Sham has been used to investigate the effects of nonlocal exchange and correlation on the Fermi surface of a simple cubic metal. The periodic lattice effects were represented by a realistic simple model pseudopotential. We find that the nonlocal terms substantially reduce the maximum Fermi-surface distortions, as experiments suggest.

Non-Local Correlation Effect on Periodic Field, Antiscreening

The role of electron-electron correlation effects in determining the energy spectrum near the first energy gap in alkali metals is investigated by the use of the propagator formalism. The correction of potential due to its screening effect is unimportant and negligible. The vertex correction which corresponds to the charge renormalization in field theory has an important role of antiscreening and makes the energy gap larger. The evaluation of the vertex correction is made to the first order diagrams of the effective Coulomb interaction. The enhancement of the energy gap at the center of the zone boundary due to the vertex correction amounts to an order of ten percent of the calculated energy gap in the OPW method in the case of lithium metal. The Fermi surface of the valence electron in lithium is pulled nearer to the zone boundary in the direction ≪110> and the distortion due to the vertex correction amounts to a few percent of the Fermi momentum. It is essential for the problem of zone-contact in lithium metal to take into account the vertex correction in the calculation of the energy band.

On the Structure of Generalized Fokker-Planck Equation of a High Temperature Plasma

The structures of the generalized Fokker-Planck equation derived in the previous pub­ lication (quoted as I) are examined in detail by considering the motion of electron beam in a high temperature electron plasma. The dynamical shielding factor provides the basis of a unified theory of the plasma oscillations. and the static shielding of the particles inter­ action in the plasma. The friction and diffusion coefficient are cakulated by taking into consideration the non-local space-time correlation effect. It is shown that the non-local correlation effect substantially modifies the contributions of the plasmon emission process. Rough estimation of the friction coefficient shows that the non-local correlation effect may increase the amount of the frictional drag at higher velocity. This effect may be essential to resolve the Langmuir paradox.