Theoretical Framework for Electronic & Optical Excitations, the GW & BSE Approximations and Considerations for Practical Calculations

Transcription

1 Theoretical Framework for Electronic & Optical Excitations, the GW & BSE Approximations and Considerations for Practical Calculations Mark S Hybertsen Center for Functional Nanomaterials Brookhaven National Laboratory HoW exciting! Hands-on Workshop on Excitations in Solids 2012 CECAM, Berlin, Germany Work supported by Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy. CECAM, Berlin, 8/4&6/12 1

2 Do you speak GW? 1965: Hedin develops an approach for systematic approximations for the electron self energy operator in many-body perturbation theory that naturally includes screening. Lowest order term: Σ = igw 1980 s & 1990 s: Reliable calculations for real materials emerge & GW works! Methodologies diversify & technical questions bubble 2000 s to today: Which GW? G 0 W 0, GW 0, G 0 W, GW, self consistency, vertex corrections, 2010s: Efficiency: Complexity one order higher than ground state (at least) CECAM, Berlin, 8/4&6/12 2

3 Resources Books for fundamentals of many-body physics techniques and applications Fetter and Walecka, Quantum Theory of Many-Particle Systems (Dover) Old school: excellent formal development Mahan, Many Particle Physics (3 rd edition) Common text-book: more focused on exemplary MB problems Haug and Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (2 nd edition, Springer) Focused on non-equilibrium theory and applications Review articles Hedin and Lundqvist, Solid State Physics, vol. 23, pp , 1969 Strong exposition of fundamentals; no optics / BSE; materials discussion dated & limited Aulbur, Jonsson and Wilkins, Solid State Physics, vol. 54, pp , 2000 Reviews fundamentals; discussion of computational issues c2000; no optics / BSE; diverse materials examples Onida, Reining and Rubio, Rev. Mod. Phys, vol. 74, pp , 2002 Includes both GW and BSE; includes TD-DFT; materials examples and exposition emphasize optics CECAM, Berlin, 8/4&6/12 3

4 Introduction: Electronic Excitations Outline for Lecture I Theoretical Framework: Green s Function Approach Hedin s Equations & the GW Approximation (1965) Physical Ingredients, Practical Considerations for Real Materials & Illustrative Examples (c1990) CECAM, Berlin, 8/4&6/12 4

5 Independent Electron Model Neutral atom or molecule Electrons sequentially fill discrete quantum mechanical levels a la Fermi Prototypical electronic excitation: Ionization energy threshold: IP = E(N-1) E(N) vac E vac E N electrons N 1 electrons Metallic solid Electrons sequentially fill a continuum of Bloch wave states below the Fermi Energy Prototypical electronic excitations: Thermal distribution of electrons & holes Fundamental to conductivity, heat capacity, E k y E F k Also characterized by electron removal energies (photoemission spectra) k x CECAM, Berlin, 8/4&6/12 5

6 Independent Electron Model: Empirical Pseudopotentials Ingredients The low order fourier components, screened local potential: V loc (G) Angular momentum resolved, atom centered potentials (non-local): V nl (k+g,k+g ) Fit key transition energies (e.g. 11 parameters, including spin-orbit, for InP) Results for semiconductors Full band structure & optical spectra Good agreement w/ photoemission Adequate band masses Similar approach for metals Fermi surfaces Chelikowsky & Cohen PRB, 1976 CECAM, Berlin, 8/4&6/12 6

7 Confronting the Many Interacting Electrons one-body electron-electron Coulomb interaction Many-body Physics Landau Fermi Liquid Theory Low energy properties of the interacting system described by quasiparticle excitations with weak residual interactions Emphasis on Model Hamiltonians Quantum Monte Carlo Methods Ab initio Materials & Chemistry Density Functional Theory Hartree-Fock + Configuration Interaction Theory Singles, doubles, Coupled-cluster Theory Many-Body Perturbation Theory Quantum Monte Carlo Methods CECAM, Berlin, 8/4&6/12 7

8 Hohenberg-Kohn-Sham Density Functional Theory Ground state energy universal functional of electron density variational Fictitious system of independent particles in an effective potential Today: many approximate functionals (LDA, GGA, Hybrids, ) efficient theory for ground state properties CECAM, Berlin, 8/4&6/12 8

9 Density Functional Theory What about the Kohn-Sham bandstructure? Except for the highest occupied state, no physical meaning! In practice, often a good guide, but band gaps wrong! Reliable DFT for bulk Silicon Hamann, PRL, 1979 Fundamental: there is a discontinuity in δexc/δn E g ( E( N + 1) E( N )) ( E( N ) E( N 1) ) = ε g KS + xc =, Sham & Schluter, PRL, 1983; Perdew & Levy, PRL, 1983 Note: Density matrix functional theory different Recent work of Wei Tao Yang Silicon Expt: 1.17 ev LDA: ~0.5 ev KS: 0.66 ev xc : 0.58 ev Godby, Schluter & Sham, PRL, 1986 CECAM, Berlin, 8/4&6/12 9

10 Hartree-Fock (Mean-Field) Theory Postulate a variational wavefunction: Slater determinant form Condition on the spin-orbitals to optimize the ground-state energy: CECAM, Berlin, 8/4&6/12 10

11 Hartree-Fock (Mean-Field) Theory Resulting in the HF equations for the orbitals exchange interaction Mean-field theory with independent orbital occupation by pairs of electrons (spin restricted Hartree-Fock) Adequate for accurate molecular structure in chemistry Poor binding energies, CECAM, Berlin, 8/4&6/12 11

12 Hartree-Fock (Mean-Field) Theory Koopman s Theorem for Electronic Excitations: E vac Condition: no orbital relaxation (self consistent change in {φ n } for the ion) Low accuracy for ionization levels in molecules N 1 electrons Semiconductors: Eg too large CECAM, Berlin, 8/4&6/12 12

13 Hartree-Fock (Mean-Field) Theory: Metals Electron-gas Model k y k x Σ x (k) (ev) Σ x k/k F ε k - E F (ev) free Dispersion k/k F HF DOS (arb) Density of States free E - E F (ev) HF CECAM, Berlin, 8/4&6/12 13

14 Outline for Today Introduction: Electronic Excitations Electronic excitations: electronic addition or removal energies Particle like excitations ( Quasiparticles ) fundamental to understand solids Correlation beyond mean-field (HF) is essential The KS eigenvalues are not a fundamentally sound approach Theoretical Framework: Green s Function Approach Hedin s Equations & the GW Approximation (1965) Physical Ingredients & Practical Considerations for Real Materials & Illustrative Examples (c1990) CECAM, Berlin, 8/4&6/12 14

15 Green s Function Framework: Physical Motivation Physical impact of electron-electron interactions: k y k x Finite lifetime k y k x Energy & momentum conservation Γ k ~ (E k -E F ) 2 Quasiparticle excitation energies: Probability incoherent No interactions Γ QP Distribution for injected electron with interactions E QP E CECAM, Berlin, 8/4&6/12 15

16 Single Particle Green s Function in Many-Body Theory One particle Green s function, N-electron system: Temporal & spatial evolution of an added electron Note 2 nd quantization: ψ a field operator Lehmann representation & excitation energies: Amplitudes from exact excited states s of N+1 / N-1 electron systems: Set {f s (r)} complete, but not orthonormal Spectral representation: Poles of ImG correspond to excitations CECAM, Berlin, 8/4&6/12 16

17 Green s Function: Equation of Motion One-body case: Spectral representation: Solutions of the homogeneous (Schroedinger) equation: Including infinitesimal to distinguish forward/backward propagation: Spectral function Density of states: CECAM, Berlin, 8/4&6/12 17

18 MBPT: Single Particle Green s Function Define self energy operator to satisfy the one particle Green s function: Equation of motion Self energy operator Σ depends on G, v(r,r ) Requires approximate treatment Generally complex & non-hermitian Another spectral representation: Homogeneous solutions Green s function {v k,e (r)} left solutions; form biorthogonal/complete set with {u k,e (r)} ε k,e complex Set of solutions needed for every energy E CECAM, Berlin, 8/4&6/12 18

19 Green s Function: Quasiparticle Equation Focus on the energy region near the quasiparticle energies: Evaluate Σ at the quasiparticle energy Self energy non-hermitian E k complex Fundamental Equation ImG k (E) Γ QP Spectral Density A(E) = π -1 ImG(E) incoherent E QP E CECAM, Berlin, 8/4&6/12 19

20 Outline for Today Introduction: Electronic Excitations Theoretical Framework: Green s Function Approach Electronic excitations are the poles in G(E) Natural framework to account for interactions & finite quasiparticle lifetime Correlation effects are collected in the still to be determined non-local, energy dependent electron self energy operator ImG k (E) E QP Γ QP E Hedin s Equations & the GW Approximation (1965) Physical Ingredients & Practical Considerations for Real Materials & Illustrative Examples (c1990) CECAM, Berlin, 8/4&6/12 20

21 Physical Theory for the Self Energy Σ Standard perturbation expansion in v(r,r ): First term is the exchange operator from HF theory v G 0 Exercise: Derive standard HF expression using G 0 from independent particles Going to higher order convergent only in the (unphysically) high density limit Natural question: What about screening v? Short range effective potential in a metal Thomas-Fermi screening model CECAM, Berlin, 8/4&6/12 21

22 Self energy operator: Exact, Closed Equations Including Σ Derived following Martin & Schwinger: Hedin, 1965 Polarizability (screening): Screened Coulomb interaction: Vertex function: GW: Throw away the hardest part CECAM, Berlin, 8/4&6/12 22

23 GW: Lowest Order Approximation Vertex function: Relative to HF, what s new in a nut-shell: Screening: v(r-r ) W(r,r ; ω) Full Green s function lines: G0 G Polarizability (screening): Random phase approximation Screened Coulomb interaction: W = v Self energy operator: G W Hedin, Exchange + correlation CECAM, Berlin, 8/4&6/12 23

24 Screened Coulomb Interaction Self consistent screening response (Hartree level): + = Express via dielectric matrix: With planewave basis: Imε 1 (ω) plasmon Nota Bene: irreducible P here often termed P 0 or χ 0 e-h continuum ω CECAM, Berlin, 8/4&6/12 24

25 Fourier transform: Anatomy of GW G W Insert general, spectral representations: Suppress real-space indices Two terms in the GW self energy operator: screening of exchange Coulomb hole CECAM, Berlin, 8/4&6/12 25

26 Anatomy of GW: QP Approximation for G GW self energy operator: screening of exchange Coulomb hole Assume independent electron (QP) model for G: Energy independent effective potential G Simplify & use definition of B(E): Note sum on all states CECAM, Berlin, 8/4&6/12 26

27 Full COH term: Anatomy of GW: Static Limit Energy independent COHSEX Approximation: Hedin, 1965 Imε 1 (ω) plasmon Static limit of screened interaction (ω p large): e-h continuum ω Polarization energy, electron at r CECAM, Berlin, 8/4&6/12 27

28 Example: GW for Electron Gas Screened Coulomb interaction: Lindhard ε -1 (q,ω) Quasiparticle equation solutions: Planewaves φ k (r) ~ e ik r A(k,E), r s =5 Hedin & Lundqvist, 1969 CECAM, Berlin, 8/4&6/12 28

29 Start of Lecture II Introduction: Electronic Excitations Theoretical Framework: Green s Function Approach Hedin s Equations & the GW Approximation (1965) The Σ=iGW emerges from the iterative solution of a closed set of equations that formally solve the many-body problem Compared to HF, there is dynamical screening of the exchange & the polarization energy gain around the added electron (COH) In principle, the G & the W that enter are the fully interacting Green s function and screened Coulomb interaction G W Physical Ingredients & Practical Considerations for Real Materials & Illustrative Examples (c1990) CECAM, Berlin, 8/4&6/12 29

30 Application to Real Materials: Key Ingredients Best independent electron (QP) model for G: LDA, Hybrid, COHSEX, Iterate on spectrum Best dielectric matrix in the RPA: Complete linear response matrix needed, e.g. from DFT More details later Matrix elements of the self energy for target states: Note Vref may be Vxc in LDA, Hybrid, CECAM, Berlin, 8/4&6/12 30

31 Dielectric Matrix: Qualitative Effects Atomic scale modulation of screening: ε Local Field effects ( r, r ) ε ( r r ) 1 1 Dynamic screening: Full w dependence vs generalized plasmon pole models Hybertsen & Louie, PRB, 1986 ω CECAM, Berlin, 8/4&6/12 31

32 Application to Materials: Key Physical Effects Local fields in screening increase the band gaps Valence band states typically in a different region of the cell from conduction band states Bulk Silicon Static COHSEX approximation over estimates band gaps Short wavelength contributions to COH term 2x too big Dynamic renormalization modest, but quantitatively important Values of Z ~ 0.8 for semiconductors QP wavefunctions often very close to KS wavefunctions Enables 1 st order treatment of Σ(r,r ;E) Hybertsen & Louie, PRL, 1985 CECAM, Berlin, 8/4&6/12 32

33 Silicon Bandstructure: 1976 to 1986 The Gold Standard The New Wave Chelikowsky & Cohen, PRB, 1976 Hybertsen & Louie, PRB, 1986 CECAM, Berlin, 8/4&6/12 33

34 Broad Applicability Semiconductors & Insulators Surfaces Si(111):2x1 Northrup, Hybertsen & Louie, PRL, 1991 C60, Molecules, Louie & Rubio, Handbook of Materials Modeling, Springer, 2005 But Significant Challenges CECAM, Berlin, 8/4&6/12 34

35 Flow for GW Calculation Ground state calculation for physical structure Input spectrum and wavefunctions from reference H Often use DFT (LDA, hybrid, ) Must calculate a large number of empty states Much more expensive in computer time than standard ground state Calculation of the full dielectric screening response Must include the full matrix up to a cut-off (control for final quality) Includes sums on empty states (control for final quality) Either full frequency dependence, or input to a plasmon pole model Typically scales as N^4 (number of atoms) self consistency Calculation of QP energy corrections from matrix elements of Σ Includes sums on empty states (control for final quality) Scales with number QP energies needed (more for any type of self consistency) Scaling w/ system size varies, but like N^4 to support self consistency QP wavefunctions needed CECAM, Berlin, 8/4&6/12 35

36 Outline for Lecture II GW: Physical Ingredients & Practical Considerations for Real Materials & Illustrative Examples (c1990) Best G - Best W approach Key role for local fields and dynamical corrections GW works for many materials at this level of implementation High cost: system size scaling; the necessity to converge sums on empty states Background: Collective & Optical Excitations Theoretical Framework: Bethe-Salpeter Equation BSE: Illustrative Examples for Specific Materials Cutting-Edge Issues for GW/BSE Theory CECAM, Berlin, 8/4&6/12 36

37 Introduction to Collective Excitations Elementary argument: Electric field: Restoring force: Oscillation freq: ω p x σ=nex Simple relationship to the dielectric function: Macroscopic screening function: Density response: Unforced oscillations at zeros of ε M (q,ω) Physical probe: Energy loss spectra for fast, charged particles Q CECAM, Berlin, 8/4&6/12 37

38 Examples 40 Lindhard: q=0.2k F at rs=2 Bulk Silicon Re(ε(q,ω)) 0-40 Im(ε 1 (q,ω)) broadened for display ω (ev) Philipp & Ehrenreich, Phys Rev, 1963 CECAM, Berlin, 8/4&6/12 38

39 Independent Electron Model: Absorption RPA express, irreducible polarizability (solid): Macroscopic ε M includes local fields from matrix inversion: Imaginary part corresponds exactly to electron-hole generation rate (optical absorption in the q 0 limit) Note: subtlety of longitudinal versus transverse response (the same for cubic crystals) E k CECAM, Berlin, 8/4&6/12 39

40 Independent Electron Model: Absorption Illustration of Local Fields: Local polarization response to a uniform applied E-field Exciton effects are missing Shape / oscillator strength -- semiconductor optical spectra Bulk Silicon E-field Hanke & Sham, PRL, 1979 Hybertsen & Louie, PRB, 1987 CECAM, Berlin, 8/4&6/12 40

41 Outline GW: Physical Ingredients & Practical Considerations for Real Materials & Illustrative Examples (c1990) Background: Collective & Optical Excitations Zeros of the macroscopic dielectric function collective excitations (plasmons) Imaginary part of the macroscopic dielectric function particle-hole excitations Exciton (electron-hole interaction) effects missing from RPA Theoretical Framework: Bethe-Salpeter Equation BSE: Illustrative Examples for Specific Materials Cutting-Edge Issues for GW/BSE Theory CECAM, Berlin, 8/4&6/12 41

42 BSE Resources Some key literature references Elliott, Phys Rev 108, 1384 (1957). Classic treatment of excitons at the band edge of semiconductors Sham & Rice, Phys Rev 144, 708 (1966) The first bridge between BSE and the effective-mass treatment of excitons Del Sole & Fiorino, Phys Rev B 29, 4631 (1984) Sorts out the longitudinal versus transverse field issue & clarifies that the local fields are properly included in the widely used BSE expression Strinati, Phys Rev B 29, 5718 (1984) Concise exposition of the basic many-body expressions leading up to the BSE Rohlfing & Louie, Phys Rev B 62, 4927 (2000) Clear exposition of the implementation of BSE Onida, Reining and Rubio, Rev. Mod. Phys, vol. 74, pp , 2002 Includes both GW and BSE; includes TD-DFT; materials examples and exposition emphasize optics Older book: R.S. Knox, Theory of Excitons, Solid State Physics Supplement Vol 5, 1963 More physical exposition, including TD-HF CECAM, Berlin, 8/4&6/12 42

43 Vertex Corrections: Electron-Hole Interactions Recall the vertex function from Hedin s closed equation set: Approximate from GW: Simplified self-consistent vertex equation: CECAM, Berlin, 8/4&6/12 43

44 Vertex Corrections: Electron-Hole Interactions Simplified self-consistent vertex equation: Iterate to see the structure: Γ 3 = Note: stop doubling all the G & W lines! CECAM, Berlin, 8/4&6/12 44

45 Vertex Corrections to Polarization: Ladder Diagrams Incorporate into the polarization: = Which goes into the final screened Coulomb interaction (dielectric function): = CECAM, Berlin, 8/4&6/12 45

46 Solution Strategy: Spectral Representation in e/h Pairs Generalize to represent part of the two particle Green s function that satisfies the BSE integral equation: exchange Graphical schematic for the BSE: 4 5 screened e/h 1 1 L = + L 0 L L 2 2 CECAM, Berlin, 8/4&6/12 46

47 General BSE Expressions Electron/hole basis set for homogeneous equation: Full BSE equations: Comments: Resonant & anti-resonant terms coupled Frequency self consistency required if dynamical screened interaction retained Notation following Rohlfing & Louie, PRB, 2000 CECAM, Berlin, 8/4&6/12 47

48 Widely Used Simplifications Assume K AB small & decouble A/B to have a single eigenvalue equation Tamm-Dancoff approximatio (commonly used in TD-DFT also) Assume static screening only Restrict to zero center of mass momentum excitons E k e/h exchange screened e/h attraction Final optical response function (absorption): Nota Bene: matrix element includes coherent exciton effects CECAM, Berlin, 8/4&6/12 48

49 Outline GW: Physical Ingredients & Practical Considerations for Real Materials & Illustrative Examples (c1990) Background: Collective & Optical Excitations Theoretical Framework: Bethe-Salpeter Equation Start from GW input quasiparticle energies BSE derived equations of motion for excitons that include screened e/h attraction and bare e/h exchange Direct connection to optical absorption including local field effects BSE: Illustrative Examples for Specific Materials Cutting-Edge Issues for GW/BSE Theory CECAM, Berlin, 8/4&6/12 49

50 Example: Bulk GaAs Basis set: (3 val)x(6 cond)x(500 k) = 9000 fcns Energy spacing about 0.15 ev Matrix element (K AA,d, K AA,x ) dominate Interpolation scheme used BSE Expt No e/h Dramatic change in oscillator strength: NOTE: In the continuum (above gap), states do NOT shift: Spectral weight (matrix elements) change due to electron-hole correl. Bound exciton states appear in the gap with scale ~ mev: Requires ~1000 k-points near Γ to resolve the Wannier excitons in k-space Rohlfing & Louie, PRL, 1998; PRB, 2000 CECAM, Berlin, 8/4&6/12 50

51 Exciton Binding & Character in Organic Crystals Anthracene Singlet: 0.64 ev Triplet: 1.86 ev Pentacene Singlet: 0.3 ev Triplet: 1.1 ev singlet singlet triplet Hummer, Puschnig & Ambrosch-Draxl, PRL, 2004 Tiago, Northrup & Louie, PRB, 2003 CECAM, Berlin, 8/4&6/12 51

52 Rutile TiO 2 Optical Spectra Expt GW/BSE Kang & Hybertsen, Phys Rev B 82, , 2010 Expt: Cardona and Harbeke, Phys Rev 137, A1467, 1965 Neglect of e-phonon interaction: Lowest (dipole dark) exciton 0.2 ev too high compared to spectroscopy Exciton binding scale much too big Oscillator strength issue near 8 ev: Other oxides: Schleife, et al, PRB, 2009 Tamm-Dancoff issue? Experimental analysis? CECAM, Berlin, 8/4&6/12 52

53 Key Materials Challenges for MBPT Application to complex bulk solids, point defects, & heterogeneous interfaces Will MBPT be a useful tool for materials discovery? Need & utility for a calibrated, static model that goes beyond hybrid functionals, but with no explicit sums on empty states Fundamental investigation of the impact of electron-phonon coupling on quasiparticle & optical excitations in titinates & related H 2 O GaN Shen, Small, Wang, Allen, Fernandez- Serra, Hybertsen, & Muckerman, J Phys Chem C 114, 13695, 2010 Classic example of intermediate to strong coupling Pascual, Camassel and Mathieu, Phys Rev Lett, 1977; Phys Rev B, 1978 CECAM, Berlin, 8/4&6/12 53

54 Outline GW: Physical Ingredients & Practical Considerations for Real Materials & Illustrative Examples (c1990) Background: Collective & Optical Excitations Theoretical Framework: Bethe-Salpeter Equation BSE: Illustrative Examples for Specific Materials Tamm-Dancoff + static screening remarkably successful for optical absorption Challenges with BZ sampling and other convergence Cutting-Edge Issues for GW/BSE Theory CECAM, Berlin, 8/4&6/12 54

55 Example: Monoclinic VO 2 Band Gap LDA: Ground state structure T > 340 K: Metallic Rutile GW: QP energies Self consistent φ k (COHSEX level) T < 340 K: Insulating Monoclinic Gatti, Bruneval, Olevano & Reining, PRL, 2007 Eyert, Ann Phys, 2002 CECAM, Berlin, 8/4&6/12 55

56 GW: To Be Self Consistent or Whether Tis Nobler Hedin s deriviation: Dressed G x Dressed W In Baym-Kadinoff theory: GW is a conserving approximation when full self consistent Charge is conserved, etc. Electron gas studies Holm & von Barth, PRB, 1998; 1999 The notation G0W0, GW0, etc, refers to which component is at least parially self consistent Self consistent, GW gives excellent total energies Self consistent, GW gives unphysical spectral functions Note: Unlike the total energy, there are no numerically exact results for A(E) Applications to real materials Quasiparticle selfconsistency Kotani, van Schilfgaarde & Faleev, PRB, 2007 Qualitative arguments: Self consistency without vertex corrections unphysical Concrete proposal for a best Veff derived from QP part of Σ Most widely used type of self consistency, generally increasing gaps CECAM, Berlin, 8/4&6/12 56

57 Impact of Self Consistency fxc in W only Van Schilfgaarde, Kotani & Faleev, PRL, 2006 Shishkin, Marsman & Kresse, PRL, 2007 CECAM, Berlin, 8/4&6/12 57

58 ZnO: The Bete Noir of GW Numerical Convergence Model for Dynamic Screening Shih, et al, PRL, 2010 Common example arguing for self consistency, Stankovski, et al, PRB, 2011 CECAM, Berlin, 8/4&6/12 58

59 Reflections Why did GW emerge in the 1980 s? Reliability of electronic structure methods (pseudopotential & other) The relative simplicity of GW in a planewave basis & the ability to numerically converge the calculations for basic materials The rapid validation by a second, independent group (Godby, Schluter & Sham) Convincing evidence that the band-gap problem in DFT was real For many materials, Best G, Best W approach is adequate Why do we ask Which GW in the 2010 s? Struggles with numerical convergence, particularly with respect to empty states On-going dialogue between pseudopotential & all-electron methods, particularly around the important role of n-1 shell core levels The real need for a physical control of the input electronic structure: Materials where KS wavefunctions are not a good approximation to QP wavefunctions More generally, the drive for a theory that is independent of DFT input or more generally does not depend on the initial guess Today GW/BSE is a vibrant field with many important groups contributing to solve big challenges CECAM, Berlin, 8/4&6/12 59