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.Comment: 9 figures, corrected typo

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

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

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

Sparse seismic imaging using variable projection

We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's function may be recovered from seismic experimental data using sparsity optimization when the source signature is known. Unfortunately, in practice this information is often missing, and must be recovered from data along with the signal using deconvolution techniques. In this paper, we present a novel methodology to simultaneously solve for the sparse signal and auxiliary parameters using a recently proposed variable projection technique. Our main contribution is to combine variable projection with sparsity promoting optimization, obtaining an efficient algorithm for large-scale sparse deconvolution problems. We demonstrate the algorithm on a seismic imaging example.Comment: 5 pages, 4 figure

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

Bodem en bemesting in de bollenteelt

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On the Age and Binarity of Fomalhaut

The nearby (d = 7.7 pc) A3V star Fomalhaut is orbited by a resolved dusty debris disk and a controversial candidate extrasolar planet. The commonly cited age for the system (200+-100 Myr) from Barrado y Navascues et al. (1997) relied on a combination of isochronal age plus youth indicators for the K4V common proper motion system TW PsA. TW PsA is 1.96 deg away from Fomalhaut, and was first proposed as a companion by Luyten (1938), but the physicality of the binarity is worth testing with modern data. I demonstrate that TW PsA is unequivocally a physical stellar companion to Fomalhaut, with true separation 0.280+0.019-0.012 pc (57.4+3.9-2.5 kAU) and sharing velocities within 0.1+-0.5 km/s -- consistent with being a bound system. Hence, TW PsA should be considered "Fomalhaut B". Combining modern HR diagram constraints with four sets of evolutionary tracks, and assuming the star was born with protosolar composition, I estimate a new isochronal age for Fomalhaut of 450+-40 Myr and mass of 1.92+-0.02 Msun. Various stellar youth diagnostics are re-examined for TW PsA. The star's rotation, X-ray emission, and Li abundances are consistent with approximate ages of 410, 380, and 360 Myr, respectively, yielding a weighted mean age of 400+-70 Myr. Combining the independent ages, I estimate a mean age for the Fomalhaut-TW PsA binary of 440+-40 Myr. The older age implies that substellar companions of a given mass are approximately one magnitude fainter at IR wavelengths than previously assumed.Comment: ApJ Letters, in press, 5 pages in emulateapj, 1 figure. Minor edits. Difference in velocity between Fomalhaut and TW PsA corrected to be 0.1+-0.5 km/

Conserving GW scheme for nonequilibrium quantum transport in molecular contacts

We give a detailed presentation of our recent scheme to include correlation effects in molecular transport calculations using the GW approximation within the non-equilibrium Keldysh formalism. We restrict the GW self-energy to the central region, and describe the leads by density functional theory (DFT). A minimal basis of maximally localized Wannier functions is applied both in the central GW region and the leads. The importance of using a conserving, i.e. fully self-consistent, GW self-energy is demonstrated both analytically and by numerical examples. We introduce an effective spin-dependent interaction which automatically reduces self-interaction errors to all orders in the interaction. The scheme is applied to the Anderson model in- and out of equilibrium. In equilibrium at zero temperature we find that GW describes the Kondo resonance fairly well for intermediate interaction strengths. Out of equilibrium we demonstrate that the one-shot G0W0 approximation can produce severe errors, in particular at high bias. Finally, we consider a benzene molecule between featureless leads. It is found that the molecule's HOMO-LUMO gap as calculated in GW is significantly reduced as the coupling to the leads is increased, reflecting the more efficient screening in the strongly coupled junction. For the IV characteristics of the junction we find that HF and G0W0[G_HF] yield results closer to GW than does DFT and G0W0[G_DFT]. This is explained in terms of self-interaction effects and life-time reduction due to electron-electron interactions.Comment: 23 pages, 16 figure