Dynamical effects in electron spectroscopy

Zhou, Jianqiang Sky; Kas, J. J.; Sponza, Lorenzo; Reshetnyak, Igor; Guzzo, Matteo; Giorgetti, C.; Gatti, Matteo; Sottile, Francesco; Rehr, J. J.; Reining, Lucia

doi:10.1063/1.4934965

Cited by 75 publications

(105 citation statements)

References 76 publications

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“…In particular, it was found that the simultaneous excitation of a plasmon and a hole leads to the emergence of 'plasmonic polaron bands', that are broadened replica of the valence bands blue-shifted by the plasmon energy. This observation was recently confirmed by theoretical and experimental work [42,43,47]. These recent developments call for a detailed analysis of cumulant expansion, as well as its relation to the standard GWA.…”

Section: Introductionmentioning

confidence: 56%

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands

et al. 2016

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PACS numbers: 71.15.Qe, 71.45.Gm Appendix A: Integral representation of cumulant seriesThe purpose of this appendix is to provide a rigorous mathematical foundation for the transformation (37) and its inverse (39) of the main text. We omit subscripts and superscripts and write simply ρ and C. Our goal is to define the mapping ρ(ν) → C(t), specify its domain and range, prove that it is one-to-one and onto, and describe its inverse map C(t) → ρ(ν). Moreover, at the end of the section we restrict our attention to a rather generic particular case that is sufficient for the application explained in the main part of this paper.Let M + (R) and M(R) respectively denote the space of finite positive measures and the space of finite signed measures on the real line (cf. Sections 1.2 and 4.1 in [1]). Indeed, an element of M(R) is simply a difference of two elements from M + (R). This space contains all absolutely integrable real-valued functions, but it also contains the "true" measures, such as absolutely summable linear combinations of Dirac delta-functions at certain points of R. For any finite signed measure ρ ∈ M(R) we interpret (37)of the main text asThis transformation is well-defined since the function (e −iνt − 1 + iνt)/ν 2 can be extended at ν = 0 in a way that it becomes a bounded continuous function on the whole real line and thus it can be integrated against the measure ρ. The basics of integration theory with respect to abstract measures can be found in the classical textbooks on measure theory, such as [1] and [2]. Let us remark that integration with respect to a general measure ρ is usually written with ρ(ν)dν replaced by dρ(ν) or ρ(dν) in mathematical literature in order to emphasize that ρ need not have a density (i.e. it could be a true measure). We will stick to the former notation, since it is also common to understand signed (or even complex) measures as particular cases of distributions (cf. Section 6.11 in [3]). * Corresponding author. Email: branko@ifs.hr Differentiation of (A1) is justified using the dominated convergence theorem (cf. Theorem 2.27(b) from [2]) and it yieldsĊ In the literature on probability theory (such as Chapter 3 of [7]), ρ is usually called the characteristic function of ρ, even though the normalization is slightly different there. Substituting t = 0 into (A1) and (A2) givesFrom (A3)-(A6) we see that an equivalent way of expressing C in terms of ρ iswith the usual convention thatIt is easy to see that C(t) is always two times continuously differentiable, but it is not true that every such function can be obtained from some ρ ∈ M(R), as we shall soon see.Now we claim that the transform defined by (A1) is a one-to-one map from M(R) to some collection of twice continuously differentiable functions, i.e. that different measures ρ map to different functions C. In order to verify that we assume ρ 1 → C and ρ 2 → C. From (A3) we get2 so the well-known fact that the Fourier-Stieltjes transform ρ → ρ is one-to-one (see Subsection VI. for any choice of points t 1 , . . . , t n ∈ R an...

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Section: Introductionmentioning

confidence: 56%

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands

et al. 2016

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“…The cumulant approach has been successful at zero T in elucidating correlation effects beyond the GW approximation of MBPT in a variety of contexts [27][28][29][30][31][32]. For example, in contrast to GW , the approach explains the multiple-plasmon satellites observed in x-ray photoemission spectra (XPS) [27,[33][34][35][36]. However, the behavior in WDM is hitherto unexplored and exhibits a number of unusual and unexpected properties.…”

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confidence: 99%

“…This form can be justified using the quasi-boson approximation [25], in which electronelectron interactions are represented in terms of electrons coupled to bosonic excitations. This approach is an improvement over GW for spectral properties [36], and is exact for certain models [42]. More elaborate GF methods exist at least in principle, including higher order MBPT [43,44], and dynamical mean-field theory with impurity Green's function's [45,46], but are more demanding computationally.…”

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Finite Temperature Green’s Function Approach for Excited State and Thermodynamic Properties of Cool to Warm Dense Matter

Kas

Rehr

2017

Phys. Rev. Lett.

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We present a finite-temperature extension of the retarded cumulant Green's function for calculations of exited-state and thermodynamic properties of electronic systems. The method incorporates a cumulant to leading order in the screened Coulomb interaction W and improves excited state properties compared to the GW approximation of many-body perturbation theory. Results for the homogeneous electron gas are presented for a wide range of densities and temperatures, from cool to warm dense matter regime, which reveal several hitherto unexpected properties. For example, correlation effects remain strong at high T while the exchange-correlation energy becomes small. In addition, the spectral function broadens and damping increases with temperature, blurring the usual quasi-particle picture. Similarly Compton scattering exhibits substantial many-body corrections that persist at normal densities and intermediate T . Results for exchange-correlation energies and potentials are in good agreement with existing theories and finite-temperature DFT functionals. Finite temperature (FT) effects in electronic systems are both of fundamental interest and practical importance. These effects vary markedly depending on whether the temperature T is larger or smaller than the Fermi temperature T F (typically a few eV). At "cool" temperatures, where T is much smaller than T F , electrons are nearly degenerate, and Fermi factors and excitations such as phonons dominate the thermal behavior [1][2][3]. In contrast thermal occupations become nearly semi-classical and electronic excitations such as plasmons become important in the warm-dense-matter (WDM) regime, where T is of order T F or larger, and condensed matter is partially ionized. Recently there has been considerable interest in both experimental and theoretical investigations of WDM for applications ranging from laser-shocked systems and inertial confinement fusion to astrophysics [4,5]. Many of these studies focus on equilibrium thermodynamic properties, e.g., using the FT generalization of density functional theory (DFT) [6][7][8]. Although in principle, FT DFT is exact [9][10][11], practical applications require exchange-correlation functionals which must be approximated, e.g., by constrained fits [12] to theoretical electron gas calculations [8,[13][14][15][16][17]. However, these approaches have various limitations. First, many materials properties such as optical and x-ray spectra depend on quasi-particle or excited-state effects. For example, band-gaps depend on quasi-particle energies, and calculations of x-ray spectra [18] and Compton scattering require correlation corrections [19]. Although methods like quantum Monte-Carlo and the random phase approximation (RPA) can provide accurate correlation energies, they are not directly applicable to such excited state properties. Secondly, currently available exchangecorrelation functionals can exhibit unphysical behavior outside the range of validity of theoretical data [20]. On the other hand Green's function (GF) methods within...

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“…This idea has been extensively explored with a time-ordered formulation of G [20,[27][28][29][30][31][32], and has been successful in describing the satellite structure in metals and semiconductors [33][34][35][36][37]. The approach restores the expected satellite progression and modifies the quasiparticle properties quantitatively.…”

Section: Introductionmentioning

confidence: 99%

Description of quasiparticle and satellite properties via cumulant expansions of the retarded one-particle Green's function

2016

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A new cumulant-based GW approximation for the retarded one-particle Green's function is proposed, motivated by an exact relation between the improper Dyson self-energy and the cumulant generating function. Qualitative aspects of this method are explored within a simple one-electron independent phonon model, where it is seen that the method preserves the energy moment of the spectral weight while also reproducing the exact Green's function in the weak coupling limit. For the three-dimensional electron gas, this method predicts multiple satellites at the bottom of the band, albeit with inaccurate peak spacing. However, its quasiparticle properties and correlation energies are more accurate than both previous cumulant methods and standard G 0 W 0 . Our results point to new features that may be exploited within the framework of cumulant-based methods and suggest promising directions for future exploration and improvement of cumulant-based GW approaches.

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Dynamical effects in electron spectroscopy

Cited by 75 publications

References 76 publications

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands

Finite Temperature Green’s Function Approach for Excited State and Thermodynamic Properties of Cool to Warm Dense Matter

Description of quasiparticle and satellite properties via cumulant expansions of the retarded one-particle Green's function

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