Vertex corrections for positive-definite spectral functions of simple metals

We present a systematic study of vertex corrections in the homogeneous electron gas at metallic densities. The vertex diagrams are built using a recently proposed positive-definite diagrammatic expansion for the spectral function. The vertex function not only provides corrections to the well known plasmon and particle-hole scatterings, but also gives rise to new physical processes such as generation of two plasmon excitations or the decay of the one-particle state into a two-particles-one-hole state. By an efficient Monte Carlo momentum integration we are able to show that the additional scattering channels are responsible for the bandwidth reduction observed in photoemission experiments on bulk sodium, appearance of the secondary plasmon satellite below the Fermi level, and a substantial redistribution of spectral weights. The feasibility of the approach for first-principles band-structure calculations is also discussed

Ultra-nonlocality in density functional theory for photo-emission spectroscopy

We derive an exact expression for the photo-current of photo-emission spectroscopy using time-dependent current density functional theory (TDCDFT). This expression is given as an integral over the Kohn-Sham spectral function renormalized by effective potentials that depend on the exchange-correlation kernel of current density functional theory. We analyze in detail the physical content of this expression by making a connection between the density-functional expression and the diagrammatic expansion of the photo-current within many-body perturbation theory. We further demonstrate that the density functional expression does not provide us with information on the kinetic energy distribution of the photo-electrons. Such information can, in principle, be obtained from TDCDFT by exactly modeling the experiment in which the photo-current is split into energy contributions by means of an external electromagnetic field outside the sample, as is done in standard detectors. We find, however, that this procedure produces very nonlocal correlations between the exchange-correlation fields in the sample and the detector.Comment: 11 pages, 11 figure

Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas

We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a straightforward inclusion of vertex diagrams beyond the GW approximation. Our approach consists of a two-steps procedure: we first express the approximate many-body self-energy as a product of half-diagrams and then identify the minimal number of half-diagrams to add in order to form a perfect square. The resulting self-energy is an unconventional sum of self-energy diagrams in which the internal lines of half a diagram are time-ordered Green's functions whereas those of the other half are anti-time-ordered Green's functions, and the lines joining the two halves are either lesser or greater Green's functions. The theory is developed using noninteracting Green's functions and subsequently extended to self-consistent Green's functions. Issues related to the conserving properties of diagrammatic approximations with positive spectral functions are also addressed. As a major application of the formalism we derive the minimal set of additional diagrams to make positive the spectral function of the GW approximation with lowest-order vertex corrections and screened interactions. The method is then applied to vertex corrections in the three-dimensional homogeneous electron gas by using a combination of analytical frequency integrations and numerical Monte-Carlo momentum integrations to evaluate the diagrams.Comment: 19 pages, 19 figure

First-principles nonequilibrium Green's function approach to transient photoabsorption: Application to atoms

We put forward a first-principle NonEquilibrium Green's Function (NEGF) approach to calculate the transient photoabsorption spectrum of optically thin samples. The method can deal with pump fields of arbitrary strength, frequency and duration as well as for overlapping and nonoverlapping pump and probe pulses. The electron-electron repulsion is accounted for by the correlation self-energy, and the resulting numerical scheme deals with matrices that scale quadratically with the system size. Two recent experiments, the first on helium and the second on krypton, are addressed. For the first experiment we explain the bending of the Autler-Townes absorption peaks with increasing the pump-probe delay \t, and relate the bending to the thickness and density of the gas. For the second experiment we find that sizable spectral structures of the pump-generated admixture of Kr ions are fingerprints of {\em dynamical correlation} effects, and hence they cannot be reproduced by time-local self-energy approximations. Remarkably, the NEGF approach also captures the retardation of the absorption onset of Kr$^{2+}$ with respect to Kr$^{1+}$ as a function of \t.Comment: 13 pages, 8 captioned figure

Diagrammatic expansion for positive density-response spectra: Application to the electron gas

In a recent paper [Phys. Rev. B 90, 115134 (2014)] we put forward a diagrammatic expansion for the self-energy which guarantees the positivity of the spectral function. In this work we extend the theory to the density response function. We write the generic diagram for the density-response spectrum as the sum of partitions. In a partition the original diagram is evaluated using time-ordered Green's functions (GF) on the left-half of the diagram, antitime-ordered GF on the right-half of the diagram and lesser or greater GF gluing the two halves. As there exist more than one way to cut a diagram in two halves, to every diagram corresponds more than one partition. We recognize that the most convenient diagrammatic objects for constructing a theory of positive spectra are the half-diagrams. Diagrammatic approximations obtained by summing the squares of half-diagrams do indeed correspond to a combination of partitions which, by construction, yield a positive spectrum. We develop the theory using bare GF and subsequently extend it to dressed GF. We further prove a connection between the positivity of the spectral function and the analytic properties of the polarizability. The general theory is illustrated with several examples and then applied to solve the long-standing problem of including vertex corrections without altering the positivity of the spectrum. In fact already the first-order vertex diagram, relevant to the study of gradient expansion, Friedel oscillations, etc., leads to spectra which are negative in certain frequency domain. We find that the simplest approximation to cure this deficiency is given by the sum of the zero-th order bubble diagram, the first-order vertex diagram and a partition of the second-order ladder diagram. We evaluate this approximation in the 3D homogeneous electron gas and show the positivity of the spectrum for all frequencies and densities.Comment: 19 pages, 19 figure

Charge dynamics in molecular junctions: Nonequilibrium Green's Function approach made fast

Real-time Green's function simulations of molecular junctions (open quantum systems) are typically performed by solving the Kadanoff-Baym equations (KBE). The KBE, however, impose a serious limitation on the maximum propagation time due to the large memory storage needed. In this work we propose a simplified Green's function approach based on the Generalized Kadanoff-Baym Ansatz (GKBA) to overcome the KBE limitation on time, significantly speed up the calculations, and yet stay close to the KBE results. This is achieved through a twofold advance: first we show how to make the GKBA work in open systems and then construct a suitable quasi-particle propagator that includes correlation effects in a diagrammatic fashion. We also provide evidence that our GKBA scheme, although already in good agreement with the KBE approach, can be further improved without increasing the computational cost.Comment: 13 pages, 13 figure

Conductance through analytic constrictions

We study the dependence of the intrinsic conductance of a nanocontact on its shape by using the recursion-transfer-matrix method. Hour-glass, torus, and spherical shapes are defined through analytic potentials, the latter two serving as rough models for ring-like and spherical molecules, respectively. The sensitivity of the conductance to geometric details is analyzed and discussed. Strong resonance effects are found for a spherical contact weakly coupled to electron reservoirs.Comment: 7 pages, 12 figure

Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model

We study time-dependent electron transport through an Anderson model. The electronic interactions on the impurity site are included via the self-energy approximations at Hartree-Fock (HF), second Born (2B), GW, and T-Matrix level as well as within a time-dependent density functional (TDDFT) scheme based on the adiabatic Bethe-Ansatz local density approximation (ABALDA) for the exchange correlation potential. The Anderson model is driven out of equilibrium by applying a bias to the leads and its nonequilibrium dynamics is determined by real-time propagation. The time-dependent currents and densities are compared to benchmark results obtained with the time-dependent density matrix renormalization group (tDMRG) method. Many-body perturbation theory beyond HF gives results in close agreement with tDMRG especially within the 2B approximation. We find that the TDDFT approach with the ABALDA approximation produces accurate results for the densities on the impurity site but overestimates the currents. This problem is found to have its origin in an overestimation of the lead densities which indicates that the exchange correlation potential must attain nonzero values in the leads.Comment: 11 pages, 9 figure

Real-time switching between multiple steady-states in quantum transport

We study transport through an interacting model system consisting of a central correlated site coupled to finite bandwidth tight-binding leads, which are considered as effectively noninteracting. Its nonequilibrium properties are determined by real-time propagation of the Kadanoff-Baym equations after applying a bias voltage to the system. The electronic interactions on the central site are incorporated by means of self-energy approximations at Hartree-Fock, second Born and GW level. We investigate the conditions under which multiple steady-state solutions occur within different self-energy approximations, and analyze in detail the nature of these states from an analysis of their spectral functions. At the Hartree-Fock level at least two stable steady-state solutions with different densities and currents can be found. By applying a gate voltage-pulse at a given time we are able to switch between these solutions. With the same parameters we find only one steady-state solution when the self-consistent second Born and GW approximations are considered. We therefore conclude that treatment of many-body interactions beyond mean-field can destroy bistability and lead to qualitatively different results as compared those at mean-field level.Comment: 10 pages, 8 figures, Submitted at "Progress in Nonequilibrium Green's Functions IV" conferenc

Correlation effects in bistability at the nanoscale: steady state and beyond

The possibility of finding multistability in the density and current of an interacting nanoscale junction coupled to semi-infinite leads is studied at various levels of approximation. The system is driven out of equilibrium by an external bias and the non-equilibrium properties are determined by real-time propagation using both time-dependent density functional theory (TDDFT) and many-body perturbation theory (MBPT). In TDDFT the exchange-correlation effects are described within a recently proposed adiabatic local density approximation (ALDA). In MBPT the electron-electron interaction is incorporated in a many-body self-energy which is then approximated at the Hartree-Fock (HF), second-Born (2B) and GW level. Assuming the existence of a steady-state and solving directly the steady-state equations we find multiple solutions in the HF approximation and within the ALDA. In these cases we investigate if and how these solutions can be reached through time evolution and how to reversibly switch between them. We further show that for the same cases the inclusion of dynamical correlation effects suppresses bistability.Comment: 13 pages, 12 figure