Diagrammatic Perturbation Theory Research Articles

Relativistic many-body perturbation theory calculations on Be, Ne 6+, Ar 14+ AND Ne

Relativistic diagrammatic perturbation theory calculations have been performed on the ground states of the beryllium atom and the isoelectronic species Ne 6+ and Ar 14+. Reference states of single-configuration Dirac-Fock wavefunctions were computed by expansion in basis sets of Gaussian functions. Second- and third-order radial correlation corrections were computed and compared to results obtained by Quiney et al. using a large basis of Slater-type functions. Second- and third-order radial and angular corrections for Ne have been computed with moderately large well-tempered Gaussian basis sets of varying expansion lengths.

A many‐body diagrammatic theory of rotation–vibration spectra

AbstractA many‐body diagrammatic perturbation theory of rotation–vibration spectra is elaborated. The present approach is based on two many‐body techniques, namely on the second quantization formalism (a rotating–vibrating molecule is formally treated here as a system of interacting vibrons, obeying the Bose–Einstein statistics) and the many‐body diagrammatic theory of a model Hamiltonian, initially suggested in the microscopic theory of nuclei and in the last decade very frequently exploited in the accounting for the correlation effects in many electron systems. In the framework of this theory, the rotation–vibration energies are determined as the eigenvalues of a finite‐dimensional model eigenproblem.

Superconducting Tc enhancement due to negative-U impurities: Monte Carlo study of a local exciton model.

The enhancement of superconductivity by a small concentration of excitonic negative-U centers is studied by a new method which combines diagrammatic perturbation theory and Monte Carlo simulation. Results are given which show how the impurity parameters should be selected in order to obtain the maximum increase in the superconducting transition temperature ${T}_{c}$. We also discuss the underlying physics of these results.

Crossover scaling in a dilute Bose superfluid near zero temperature.

The behavior of a dilute Bose superfluid at low temperatures, $Tll{T}_{\ensuremath{\lambda}}$, is considered with emphasis on the superfluid density, ${\ensuremath{\rho}}_{s}(T)$. Many of the predictions of the Bogoliubov model are exact in this regime and are shown to lead to a scaling description of the crossover from ideal to interacting Bose gas behavior as the density is reduced. Combined with previous work on scaling near criticality, $T\ensuremath{\simeq}{T}_{\ensuremath{\lambda}}$, these results complete the crossover description of the dilute superfluid over the full temperature range. Diagrammatic perturbation theory in the superfluid phase is outlined and previous results from the helium literature are summarized. The various divergences encountered have previously been shown to arise from nonanalyticities in the self-energy functions at zero momentum, and these are related to the spin-wave nature of the superfluid phase. A full renormalization-group fixed-point picture is presented summarizing the zero-temperature and finite-temperature regimes and the flows connecting them.

Hilbert space and propagator in thermal field theory.

By use of general principles (Kubo-Martin-Schwinger condition, breakdown of Lorentz invariance, triviality arguments), the nature of diagrammatic perturbation theory in relativistic field theory at nonzero temperature is investigated. By operator-algebraic techniques it is found that the conventional method is inconsistent, and an essentially unique alternative is given.

Comparison between the correlated-basis-functions method and the density-functional theory for inhomogeneous systems.

As a hypothetical inhomogeneous quantum many-body model, we take a weakly interacting Bose gas made inhomogeneous by the presence of a weak external field. The interaction is assumed to be Fourier transformable and characterized by a strength parameter \ensuremath{\lambda}; this is also true for the external field, characterized by a strength parameter \ensuremath{\varepsilon}. The ground-state energy is calculated to order ${\ensuremath{\varepsilon}}^{2}$${\ensuremath{\lambda}}^{2}$ using three methods: diagrammatic perturbation theory, correlated basis functions (CBF), and density-functional theory (DFT). The diagrammatic perturbation theoretical calculation is new. It differs from our earlier approach for homogeneous Bose systems which evolved from the Hugenholtz-Pines theory. We are able to reproduce the same results in an efficient manner. For the inhomogeneous system, the results are used to measure CBF against DFT. It is found that in their simplest forms CBF yields results which are better than the renormalized DFT by Ebner and Saam. In particular, CBF is superior to DFT in the local-density approximation, even though the latter was designed to take care of systems with slow and small density variations such as the model considered here.

Superconducting Tc enhancement due to local phonon impurities

We have studied the enhancement of superconductivity due to a small concentration of local phonon impurities using a new method. The method combines diagrammatic perturbation theory and Monte Carlo simulation. This method allows us fully to take into account the retarded nature of the interactions and hence study in detail the interplay between the electron-phonon systems of the host and the impurities.

Dynamical conductivity in the infrared from impurity scattering in a polar semiconductor.

We derive an expression for the contribution to the dynamical conductivity from impurity scattering in a polar semiconductor. The derivation is based on the Kubo formalism and diagrammatic perturbation theory. Several different derivations of the dynamical conductivity and free-carrier absorption can be found in the literature. In the few cases where the impurity contribution has been considered, in the presence of coupling to optical phonons, the results which have been published disagree with each other. The purpose of this work is to resolve this problem and to find the cause of these discrepancies.

Acoustic localization in one dimension in the presence of a flow field.

The effect of a uniform flow field on one-dimensional localized acoustical excitations is investigated by use of both the usual Feynman diagrammatic perturbation theory and the Berezinskii formalism. While leading-order perturbation theory suggests that localization is destroyed by a flow, or at least drastically modified, the Berezinskii method proves that localization suffers no essential modifications. The reason for the breakdown of the usual perturbative approach is discussed.

Superconducting Tc enhancement due to excitonic negative-U centers: A Monte Carlo study.

The enhancement of superconductivity by a small concentration of excitonic negative-U centers is studied by a new method which combines diagrammatic perturbation theory and Monte Carlo simulation. Results are given which show how the impurity parameters should be selected in order to obtain the maximum increase in the superconducting transition temperature ${\mathrm{T}}_{\mathrm{c}}$.

Spin wave damping in Heisenberg ferromagnets near the percolation threshold

The decay of zero temperature spin wave excitations near the percolation threshold in bond-diluted d-dimensional (d>1) Heisenberg ferromagnets is investigated using a Green function equation-of-motion method. The diagrammatic perturbation theory is convergent in the hydrodynamic limit (k xi <<1) and the following expression is obtained there for the damping, or decay rate: Gamma c(k, xi ) varies as (p-pc)-vd+(t- beta ) kd+2,(k xi <<1). This form satisfies the requirements of the dynamic scaling principle, by which Gamma c(k, xi )=kzg(k xi ) for general k xi , and z=2+(t- beta )/ nu . An explicit expression, applicable in the hydrodynamic regime and consistent with dynamic scaling, is also obtained for the infinite cluster transverse dynamic structure function. The approach is extended to incorporate the ensemble of finite clusters and to treat the case of non-zero temperature and also the experimentally more relevant situation of site dilution.

The polarization-function counterpoise method. An application of the diagrammatic perturbation theory to the He–H2 molecule in the region of the van der Waals minimum

The results of the calculation on the C∞v He–H2 van der Waals molecule by employing the diagrammatic many-body theory to treat the electron correlation effects are reported in this paper. The use of the partial counterpoise method to compute the self-consistent field (SCF) and correlation energies, when a moderate basis set is employed, may lead to a reliable description of the potential curve for the van der Waals (VDW) system.

Many-electron effects in multiphoton ionization: Screening effects in single-electron ionization.

We study the influence of many-electron effects in multiphoton ionization within the framework of diagrammatic many-body perturbation theory. We renormalize the electron-dipole coupling by summing to infinite order both many-electron interactions using the random-phase approximation and higher-order intensity terms. We introduce an effective intensity, which takes into account the screening of the field by the electrons and represents the intensity really seen by an electron. The theory is applied to a calculation of the two-photon one-electron ionization rate of helium in the weak-field limit, using a local-density approximation one-electron basis set. The influence of many-electron effects strongly depends on the field frequency. The two-photon ionization rate of helium is lowered at low frequency (by a factor up to 1.4) and increased at high frequency when the photon energy is above the ionization threshold. Finally, the importance of many-electron effects in multiphoton ionization (e.g., regarding inner-shell ionization) is qualitatively discussed in connection with experiments.

Theory of a Tm impurity in metals in a jj-coupling model

A Tm magnetic impurity with U= infinity is considered in the jj-coupling scheme in the limit of zero j.j coupling. The model has SU(N) symmetry. The spin-fluctuation energy scale is found in the f12 and f13 Kondo limits via Haldane scaling arguments. The model possesses a 1/N expansion; selecting the leading-N diagrams in perturbation theory, the Yafet-Varma integral equation is derived. This is solved analytically in the f1 and f2 Kondo limits and the results for N to infinity are found to be in accord with scaling theory. The energy separation between the singlet ground state and the N-fold-degenerate excited state is found as a function of f occupation in the large-N limit. The results are found to differ significantly with data on LaTmSe and YTmSe. A model with large j.j coupling is also considered and does not significantly improve the agreement.

MBPT studies of van der Waals molecules. III. The reliability of apparently accurate calculations for the magnesium dimer

The interaction potential for the magnesium dimer is calculated by using the diagrammatic many-body perturbation theory within the framework of the supermolecule approach. Different approximations for the perturbation treatment of the electron correlation effects are analysed with particular emphasis on the results of the complete fourth-order many-body perturbation theory. The influence of the composition of the basis set on the calculated interaction potentials and the basis set superposition effects are investigated. It is concluded that the interaction potentials for van der Waals systems calculated by the supermolecule technique might be highly uncertain because of the basis set superposition effects at the correlated level. The advantages and disadvantages of different methods for the calculation of the energy of weakly interacting systems are discussed in the light of their ability to cope with both the electron correlation problem and the basis set superposition effect.

Calculation of spin-density matrix by diagrammatic perturbation theory

A diagrammatic perturbation-theory method for direct calculation of spin-density matrix of open-shellN-electron systems described by the restricted Hartree-Fock one-particle functions is formulated. The formulae correct up to the second order of perturbation theory (second order in correlation effects) are presented. Their generalization to account for infinite summations of dominant correlation effects is simple, realized by making use of the so-called coupled cluster approach.

The Dirac equation in the algebraic approximation. III. Diagrammatic perturbation theory applied to a model problem

For pt.II see ibid., vol.17, no.7, p.1201 (1984). The solution of the Dirac equation for hydrogen-like atoms within the algebraic approximation, that is, by using finite basis sets, is considered. The model problem of a hydrogenic atom with nuclear charge Z perturbed by a potential-Z'/r is used to demonstrate the feasibility of including relativistic effects in diagrammatic perturbation theory calculations performed within the algebraic approximation. Both ground- and excited state calculations are reported. Particular attention is paid to the choice of basis sets and the handling of the negative-energy states. It is shown that the 'finite basis set disease' can be avoided in perturbation theory calculations by making an appropriate choice of basis sets. Negative-energy states must be included in the perturbation theory summations. The importance of this work to the development of a relativistic many-body perturbation theory of molecular electronic structure is discussed.

Diagrammatic many-body perturbation theory of atomic and molecular electronic structure

The diagrammatic many-body perturbation theory of atomic and molecular electronic structure is reviewed. Attention is centred on the formulation of the method within the algebraic approximation (that is, using finite basis sets) which allows applications to be made to atoms and molecules within a unified framework. The second section is devoted to the basic formalism of the diagrammatic many-body perturbation theory of atoms and molecules. The diagrammatic expansion of both the energy and the wavefunction are considered, the latter being more compact than the former. Section 3 is concerned with aspects of the truncation of the perturbation expansion and the use of many-body perturbation theory in the analysis and comparison of many contemporary approaches to the correlation problem is briefly outlined. The fourth section is devoted to computational aspects of many-body perturbation theory calculations. Some applications are very briefly discussed in section 5.

Van der Waals interaction potentials

Many-body contributions to van der Waals interaction potentials are discussed using the Hartree-Fock approximation as a zero-order model and diagrammatic many-body perturbation theory to describe electron correlation effects. A perturbation series is obtained for the effects of electron correlation on each of the terms in the expansion of the total interaction energy in its n-body components. Generalizations of the function counterpoise technique are used to allow for basis set superposition effects in calculations of many-body components of interaction energies. Prototype calculations are reported for the helium trimer.

Equation-of-motion treatment of the N-fold-degenerate Anderson model in the large-N limit.

The periodic Anderson model of magnetic moments within a metal is investigated in the limit of a large spin-orbit degeneracy N of the magnetic ions. It is shown, by means of the equations of motion for the single-particle Green's function, that an exactly solvable limit U\ensuremath{\rightarrow}\ensuremath{\infty} and N\ensuremath{\rightarrow}\ensuremath{\infty} (U Coulomb correlation) exists under the assumption that the spin-orbit quantum number is also a good quantum number for the conduction band or, equivalently, that there are also N conduction bands. Then it can be shown by means of diagrammatic perturbation theory that a certain decoupling on the third level of the equation-of-motion hierarchy becomes exact in the limit N\ensuremath{\rightarrow}\ensuremath{\infty}. Intersite contributions are of order 1/N, so that, except for a chemical-potential renormalization, the lattice is equivalent to ${N}_{s}$ independent impurities for N\ensuremath{\rightarrow}\ensuremath{\infty} (${N}_{s}$ number of sites). An integral equation for the one-particle Green's function, which is exact in these limits, is derived and discussed. This integral equation can be solved analytically for zero temperature. To obtain physically meaningful results one has to include 1/N corrections in which case the equation can only be solved numerically. Results for the spectral function at different temperatures in the Kondo and in the mixed-valence regime are presented. The dependence of the valency on the localized-level position and thus the transition from the Kondo to the mixed-valence regime are investigated. A suitable approximation for the case of finite U is discussed.