Diagrammatic Many-body Theory Research Articles

Effective mass of quasiparticles from thermodynamics

We discuss the potential advantages of calculating the effective mass of quasiparticles in the interacting electron liquid from the low-temperature free energy vis-a-vis the conventional approach, in which the effective mass is obtained from approximate calculations of the self-energy, or from a quantum Monte Carlo evaluation of the energy of a variational "quasiparticle wave function". While raw quantum Monte Carlo data are presently too sparse to allow for an accurate determination of the effective mass, the values estimated by this method are numerically close to the ones obtained in previous calculations using diagrammatic many-body theory. In contrast to this, a recently published parametrization of quantum Monte Carlo data for the free energy of the homogeneous electron liquid yields effective masses that considerably deviate from previous calculations and even change sign for low densities, reflecting an unphysical negative entropy. We suggest that this anomaly is related to the treatment of the exchange energy at finite temperature.

Study of attosecond delays using perturbation diagrams and exterior complex scaling

We describe in detail how attosecond delays in laser-assisted photoionization can be computed using perturbation theory based on two-photon matrix elements. Special emphasis is laid on above-threshold ionization, where the electron interacts with an infrared field after photoionization by an extreme ultraviolet field. Correlation effects are introduced using diagrammatic many-body theory to the level of the random-phase approximation with exchange. Our aim is to provide an ab initio route to correlated multi-photon processes that are required for an accurate description of experiments on the attosecond time scale. Here, our results are focused on photoionization of the M-shell of argon atoms, where experiments have been carried out using the so-called reconstruction of attosecond beating by the two-photon interference transitions technique. An influence of autoionizing resonances in attosecond delay measurements is observed. Further, it is shown that the delay depends on both detection angle of the photoelectron and energy of the probe photon.

Positron scattering and annihilation in hydrogenlike ions

Diagrammatic many-body theory is used to calculate the scattering phase shifts, normalized annihilation rates ${Z}_{\mathrm{eff}}$, and annihilation $\ensuremath{\gamma}$ spectra for positron collisions with the hydrogenlike ions He${}^{+}$, Li${}^{2+}$, B${}^{4+}$, and F${}^{8+}$. Short-range electron-positron correlations and longer-range positron-ion correlations are accounted for by evaluating nonlocal corrections to the annihilation vertex and the exact positron self-energy. The numerical calculation of the many-body theory diagrams is performed using $B$-spline basis sets. To elucidate the role of the positron-ion repulsion, the annihilation rate is also estimated analytically in the Coulomb-Born approximation. It is found that the energy dependence and magnitude of ${Z}_{\mathrm{eff}}$ are governed by the Gamow factor that characterizes the suppression of the positron wave function near the ion. For all of the H-like ions, the correlation enhancement of the annihilation rate is found to be predominantly due to corrections to the annihilation vertex, while the corrections to the positron wave function play only a minor role. Results of the calculations for $s$-, $p$-, and $d$-wave incident positrons of energies up to the positronium-formation threshold are presented. Where comparison is possible, our values are in excellent agreement with the results obtained using other, e.g., variational, methods. The annihilation-vertex enhancement factors obtained in the present calculations are found to scale approximately as $1+(1.6+0.46\ensuremath{\ell})/{Z}_{i}$, where ${Z}_{i}$ is the net charge of the ion and $\ensuremath{\ell}$ is the positron orbital angular momentum. Our results for positron annihilation in H-like ions provide insights into the problem of positron annihilation with core electrons in atoms and condensed matter systems, which have similar binding energies.

Lifetime of double occupancies in the Fermi-Hubbard model

We investigate the decay of artificially created double occupancies in a repulsive Fermi-Hubbard system in the strongly interacting limit using diagrammatic many-body theory and experiments with ultracold fermions in optical lattices. The lifetime of the doublons is found to scale exponentially with the ratio of the on-site repulsion to the bandwidth. We show that the dominant decay process in presence of background holes is the excitation of a large number of particle-hole pairs to absorb the energy of the doublon. We also show that the strongly interacting nature of the background state is crucial in obtaining the correct estimate of the doublon lifetime in these systems. The theoretical estimates and the experimental data are in agreement.

Absence of singular superconducting fluctuation corrections to thermal conductivity

We evaluate the superconducting fluctuation corrections to thermal conductivity in the normal state which diverge as T approaches T_c. We find zero total contribution for one, two and three-dimensional superconductors for arbitrary impurity concentration. The method used is diagrammatic many-body theory, and all contributions -- Aslamazov-Larkin (AL), Maki-Thompson (MT), and density-of-states (DOS) -- are considered. The AL contribution is convergent, whilst the divergences of the DOS and MT diagrams exactly cancel.

Exact diagrammatic solution for a three-level system in an intense laser field

The diagrammatic solution to a (sequentially coupled) one-electron three-level system in an intense laser field is derived. The solution is in the form of a continued-fraction expansion and is equal to the Floquet state that is adiabatically connected to the ground state. The formalism used is a recently presented diagrammatic many-body theory by Jonsson that can be used for non-perturbative calculations in strong fields. The purpose of the calculation is to demonstrate how a non-trivial one-electron problem can be solved exactly within the formalism.

Diagrammatic many-body theory for atoms in high-intensity laser fields Part I

Diagrammatic many-body theory has been used extensively in the treatment of electron–electron correlations in atomic photoionization at low intensities. We discuss how it can be used at high intensities also. The standard diagrammatic formalism is derived for time-independent interactions by using adiabatic switching. This formalism can be formally derived for harmonic fields also but leads to unphysical results for strong fields. If the amplitude function of the laser field is an exponential function, however, the standard derivation still applies. If the adiabatic limit is not taken, this time-dependent formalism can be used for any intensity. In practice one is still limited to slow turn-on, but, assuming slow turn-on, we show that for a discrete system the linked expansion, when summed to infinite order, gives the Floquet state that is adiabatically connected to the ground state. When continua are included, we find that qualitatively correct results are obtained only if one uses an expansion of the time derivative of the wave function instead of an expansion of the wave function itself. We also show that the imaginary part of the self-energies must be excluded from the energy denominators, since they otherwise lead to unphysical results. These results are found by treating model systems for which the exact solutions are known and for which the diagrams can be evaluated to any order.

Diagrammatic many-body theory for atoms in high-intensity laser fields Part II

Diagrammatic many-body theory for atoms in high-intensity laser fields Part II

Exact behavior of the density and spin susceptibilities of a Fermi liquid for large wave vectors: Derivation from diagrammatic many-body theory.

The exact asymptotic behavior of the density and spin response functions of a uniform Fermi system for large wave vectors is derived from diagrammatic many-body theory. Various exact relationships between the self-energy, the particle-hole interaction, and the vertex corrections are derived for the first time and applied to this problem. The final results agree with those provided by the kinetic equation approach. Different behavior of the polarization potentials and local-field factors for interactions that decrease faster or slower than 1/${q}^{2}$ for large wave vector q, is pointed out.

Many-body calculation of the 3p-3d x-ray emission spectrum of krypton

The 3p–3d XES spectrum of krypton is calculated by the diagrammatic many-body theory within the framework of Hartree-Fock calculations. A good agreement with experiment is obtained. Many-body effects, like screening and interference effects of the initial 3p hole on the XES spectrum, are discussed.

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.

Breakdown of the one-electron picture in 3d-1→4p-1X-ray emission spectrum of Xe

The 3d-1 to 4p-1 X-ray emission spectrum of Xe has been calculated from first principles by diagrammatic many-body theory within the framework of a free-atom calculation. The agreement of the theoretical spectrum with experiment is good. The spectrum is entirely dominated by the strong dynamical effects of a final 4p hole. The one-electron picture of a 4p hole breaks down by a strong dynamical giant Coster-Kronig 4p-1 to or from 4d-2m, epsilon f process.

Many-electron interactions in the M45-NN Auger spectrum of metallic cadmium

A broad ( approximately 25 eV FWHM) spectrum has been observed in the M45-N23N45 Auger energy region of metallic cadmium. The spectrum shows that the one-electron picture of a 4p hole in the final double-hole state breaks down completely because of strong dynamical giant Coster-Kronig 4p-1 4d-1 to or from 4d-3 epsilon f fluctuation and decay processes. The spectrum is compared with the theoretical atomic spectrum calculated by diagrammatic many-body theory. There is excellent agreement. The influence of the many-electron interactions on the M45-N1N45 and M45-N23N23 Auger spectra is discussed.

Strong dynamical effects in unusually broad Lγ 2,3emission spectra of46Pd to54Xe

The broad Lgamma 2,3 emission spectra of 46Pd to 54Xe are calculated from first principles in the framework of a free-atom calculation by using diagrammatic many-body theory. The Lgamma 2,3 emission spectra are found to be due to breakdown of the quasiparticle picture of the final 4p core hole in these elements by very strong giant Coster-Kronig 4p to or from 4d2 dipolar fluctuations and epsilon f decay processes. The calculated spectra are in good agreement with those obtained experimentally.

Many-electron effects in the 3p X-ray photoelectron spectrum of Kr

The X-ray photoelectron spectrum of Kr in the neighbourhood of the main 3p lines has been calculated using diagrammatic many-body theory for the 3p self-energy and spectral function. Super Coster-Kronig 3p to or from 3d2epsilon f dipole fluctuations are found to shift the 3p lines by about 3 eV from their Delta SCF positions, the dipole shift being approximately 30% of the Delta SCF monopole relaxation shift. For determining the 3p linewidth the 3p to 3d4s epsilon p and 3p to 3d4p epsilon d Coster-Kronig transitions and the super Coster-Kronig transitions are approximately equally important. The calculated positions and widths of the 3p main lines are in good agreement with experiment.

On the position and linewidth of M-shell vacancies in Ge to Zr: Many electron effects in 3p-core hole spectra

The X-ray photoelectron spectrum of atomic Kr in the M 2,3 (3 p) region has been calculated from first principles using diagrammatic many-body theory. Also, the variation of the M 2,3-vacancy linewidth for the surrounding elements has been studied within an atomic framework, comparing the widths in the free atom and the solid state.