Diagrammatic Many-body Perturbation Theory Research Articles

Relativistic time-dependent configuration-interaction singles method

In this work, a derivation and implementation of the relativistic time-dependent configuration interaction singles (RTDCIS) method is presented. Various observables for krypton and xenon atoms obtained by RTDCIS are compared with experimental data and alternative relativistic calculations. This includes energies of occupied orbitals in the Dirac-Fock ground state, Rydberg state energies, Fano resonances and photoionization cross sections. Diagrammatic many-body perturbation theory, based on the relativistic random phase approximation, is used as a benchmark with excellent agreement between RTDCIS reported at the Tamm-Dancoff level. Results from RTDCIS are computed in the length gauge, here the negative energy states can be omitted with acceptable loss of accuracy. A complex absorbing potential, that is used to remove photoelectrons far from the ion, is implemented as a scalar potential and validated for RTDCIS. The RTDCIS methodology presented here opens for future studies of strong-field processes, such as attosecond transient absorption and high-order harmonic generation, with electron and hole spin dynamics and other relativistic effects described by first principle via the Dirac equation.

Quantum many-body states and Green's functions of nonequilibrium electron-magnon systems: Localized spin operators versus their mapping to Holstein-Primakoff bosons

The operators of localized spins within a magnetic material commute at different sites of its lattice and anticommute on the same site, so they are neither fermionic nor bosonic operators. Thus, to construct diagrammatic many-body perturbation theory, the spin operators are usually mapped to the bosonic ones with Holstein-Primakoff (HP) transformation being the most widely used in magnonics and spintronics literature. However, to make calculations tractable, the square root of operators in the HP transformation is expanded into a Taylor series truncated to some low order. This poses a question on the range of validity of truncated HP transformation when describing nonequilibrium dynamics of localized spins interacting with each other or with conduction electron spins. Here we apply exact diagonalization techniques to Hamiltonian of fermions (i.e., electrons) interacting with HP bosons vs. Hamiltonian of fermions interacting with the original localized spin operators in order to compare their many-body states and one-particle equilibrium or nonequilibrium Green functions. The Hamiltonian of fermions interacting with HP bosons gives incorrect ground state and electronic spectral function, unless large number of terms are retained in truncated HP transformation. Furthermore, tracking nonequilibrium dynamics of localized spins over longer time intervals requires progressively larger number of terms in truncated HP transformation. Finally, we show that recently proposed [M. Vogl et al., Phys. Rev. Research 2, 043243 (2020); J. K\"{o}nig et al., SciPost Phys. 10, 007 (2021)] resummed HP transformation resolves the trouble with truncated HP transformation, while allowing us to derive an exact (manifestly Hermitian) Hamiltonian consisting of finite and fixed number of boson-boson and electron-boson interacting terms.

Approximate energy functionals for one-body reduced density matrix functional theory from many-body perturbation theory

We develop a systematic approach to construct energy functionals of the one-particle reduced density matrix (1RDM) for equilibrium systems at finite temperature. The starting point of our formulation is the grand potential Ω[G] regarded as variational functional of the Green’s function G based on diagrammatic many-body perturbation theory and for which we consider either the Klein or Luttinger–Ward form. By restricting the input Green’s function to be one-to-one related to a set on one-particle reduced density matrices (1RDM) this functional becomes a functional of the 1RDM. To establish the one-to-one mapping we use that, at any finite temperature and for a given 1RDM γ in a finite basis, there exists a non-interacting system with a spatially non-local potential v[γ] which reproduces the given 1RDM. The corresponding set of non-interacting Green’s functions defines the variational domain of the functional Ω. In the zero temperature limit we obtain an energy functional E[γ] which by minimisation yields an approximate ground state 1RDM and energy. As an application of the formalism we use the Klein and Luttinger–Ward functionals in the GW-approximation to compute the binding curve of a model hydrogen molecule using an extended Hubbard Hamiltonian. We compare further to the case in which we evaluate the functionals on a Hartree–Fock and a Kohn–Sham Green’s function. We find that the Luttinger–Ward version of the functionals performs the best and is able to reproduce energies close to the GW energy which corresponds to the stationary point.

Pad\xe9 resummation of many-body perturbation theories

In a typical scenario the diagrammatic many-body perturbation theory generates asymptotic series. Despite non-convergence, the asymptotic expansions are useful when truncated to a finite number of terms. This is the reason for the popularity of leading-order methods such as the GW approximation in condensed matter, molecular and atomic physics. Appropriate truncation order required for the accurate description of strongly correlated materials is, however, not known a priori. Here an efficient method based on the Padé approximation is introduced for the regularization of perturbative series allowing to perform higher-order self-consistent calculations and to make quantitative predictions on the convergence of many-body perturbation theories. The theory is extended towards excited states where the Wick theorem is not directly applicable. Focusing on the plasmon-assisted photoemission from graphene, we treat diagrammatically electrons coupled to the excited state plasmons and predict new spectral features that can be observed in the time-resolved measurements.

Many-body Green's function theory for electron-phonon interactions: Ground state properties of the Holstein dimer.

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is strongly correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.

New determination of double-β-decay properties in48Ca: High-precisionQββ-value measurement and improved nuclear matrix element calculations

We report a direct measurement of the Q-value of the neutrinoless double-beta-decay candidate 48Ca at the TITAN Penning-trap mass spectrometer, with the result that Q = 4267.98(32) keV. We measured the masses of both the mother and daughter nuclides, and in the latter case found a 1 keV deviation from the literature value. In addition to the Q-value, we also present results of a new calculation of the neutrinoless double-beta-decay nuclear matrix element of 48Ca. Using diagrammatic many-body perturbation theory to second order to account for physics outside the valence space, we constructed an effective shell-model double-beta-decay operator, which increased the nuclear matrix element by about 75% compared with that produced by the bare operator. The new Q-value and matrix element strengthen the case for a 48Ca double-beta-decay experiment.

Effective double-β-decay operator for76Ge and82Se

We use diagrammatic many-body perturbation theory in combination with low-momentum interactions derived from chiral effective field theory to construct effective shell-model transition operators for the neutrinoless double-beta decay of 76Ge and 82Se. We include all unfolded diagrams to first- and second-order in the interaction and all singly folded diagrams that can be constructed from them. The resulting effective operator, which accounts for physics outside the shell-model space, increases the nuclear matrix element by about 20% in 76Ge and 30% in 82Se.

Diagrammatic approach to attosecond delays in photoionization

We study laser-assisted photoionization by attosecond pulses using a time-independent formalism based on diagrammatic many-body perturbation theory. Our aim is to provide an ab inito route to the "delays" for this above-threshold ionization process, which is essential for a quantitative understanding of attosecond metrology. We present correction curves for characterization schemes of attosecond pulses, such as "streaking", that account for the delayed atomic response in ionization from neon and argon. We also verify that photoelectron delays from many-electron atoms can be measured using similar schemes if, instead, the so-called continuum--continuum delay is subtracted. Our method is general and it can be extended also to more complex systems and additional correlation effects can be introduced systematically.

Vertex enhancement of positron annihilation with core electrons

γ-spectra and annihilation rate parameters Zeff for positron annihilation on noble gas atoms are calculated using diagrammatic many-body perturbation theory. Corrections to the annihilation vertex, which describe short range electron-positron correlations, are found to cause significant enhancement for the inner shell orbitals. Using the ab initio theory, we calculate enhancement factors and annihilation fractions for all subshells.

Positron annihilation in hydrogen-like ions

Diagrammatic many-body perturbation theory is used to calculate the scattering phase shifts, annihilation rate parameters Zeff and γ-spectra for positrons annihilating on hydrogen-like ions. The enhancement of the annihilation probability above the independent-particle approximation is found to be almost entirely due to corrections to the annihilation vertex that describe electron-positron attraction at short range.

Higher excitations in coupled-cluster theory

The viability of treating higher excitations in coupled-cluster theory is discussed. An algorithm is presented for solving coupled-cluster (CC) equations which can handle any excitation. Our method combines the formalism of diagrammatic many-body perturbation theory and string-based configuration interaction (CI). CC equations are explicitly put down in terms of antisymmetrized diagrams and a general method is proposed for the factorization of the corresponding algebraic expressions. Contractions between cluster amplitudes and intermediates are evaluated by a string-based algorithm. In contrast to our previous developments [J. Chem. Phys. 113, 1359 (2000)] the operation count of this new method scales roughly as the (2n+2)nd power of the basis set size where n is the highest excitation in the cluster operator. As a by-product we get a completely new CI formalism which is effective for solving both truncated and full CI problems. Generalization for approximate CC models as well as multireference cases is also discussed.

Supermolecular approach to many-body dispersion interactions in weak van der Waals complexes: He, Ne, and Ar trimers

Using the diagrammatic many-body perturbation theory, various three-body dispersion terms that appear in the intermolecular Mo/ller–Plesset perturbation theory (MPPT) are identified and classified with regard to the effects of intramonomer electron correlation on the dispersion term. Via the connection with the supermolecular MPPT, it is demonstrated how the leading dispersion nonadditivities arise within supermolecular calculations that employ MPPT or coupled cluster formalisms. The numerical calculations for He3, Ne3, and Ar3 in triangular geometries fully confirm theoretical predictions. The calculated values of dispersion nonadditivity clearly show that the coupled cluster theory with single, double, and noniterative triple excitations provides the proper framework for the efficient inclusion of the intramonomer correlation effects in dispersion nonadditivity. The convergence of the two-body and three-body terms is shown to be very similar if we compare the three-body terms of an order higher than the two-body terms. This pattern is used to provide the estimates of the total nonadditivities in the three trimers within a few percent accuracy.

Relativistic many-body calculation of the electric dipole moment of atomic rubidium due to parity and time-reversal violation.

In this paper fully ab initio calculations of the electric dipole moment (EDM) of atomic rubidium due to two possible mechanisms---the intrinsic electric dipole moment of the electron and the scalar-pseudoscalar coupling between the electrons and the nucleons---are presented. The calculations were carried out using an approach which is a hybrid of the diagrammatic many-body perturbation theory (MBPT) and the multiconfiguration Dirac-Fock method. These calculations, unlike any of the previous MBPT calculations for the rubidium atom, also take into account the effects of electron pair correlations on the atomic EDM. Our results demonstrate that these effects can make significant contributions to the EDM of alkali-metal atoms.

On the diagrammatic analysis of electron correlation effects in atoms and molecules: Fifth-order energy components

Abstract The diagrammatic many-body perturbation theory of electron correlation effects in atoms and molecules is employed in the description of some fifth-order correlation effects.

Diagrammatic many-body perturbation expansion for atoms and molecules: IX. On the use of dynamic load balancing on a multi-processor computer

A formulation of the diagrammatic many-body perturbation theory suitable for effective implementation on multi-processor computers is described. This concurrent computation many-body perturbation theory ( ccMBPT) exploits the additive separability of the correlation energy components resulting from the linked diagram expansion to devise algorithms suitable for a parallel processing environment. A dynamic load balancing technique is employed to exploit the parallel processing capabilities of computers such as the CRAY Y-MP. The performance of the technique is demonstrated in calculations of the most computationally demanding of the fourth order energy components, those involving triply excited intermediate states. Execution rates in excess of 2.28×10 9 floating point operations per second are observed on an eight-processor machine.

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.

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.

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.

General-model-space perturbation theory: Excitation and ionization of N2

Vertical excitation and ionization energies are calculated by diagrammatic many-body perturbation theory (MBPT) for 20 states of N2 and N+2 at R=2.068 bohr. Nondegenerate or degenerate MBPT with complete or incomplete model spaces is employed, depending on the molecular state. A variety of zero-order Hamiltonians (H0) is tried. It is found that [2/1] Padé approximants depend little on the choice of H0, making them superior to straightforward summation to third order. They also provide good approximations to the CI limit for the basis (average error for all states 0.35 eV).