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We present a fully self-consistent combined GW and dynamical mean field(GW+DMFT) study of the spectral properties of the extended two-dimensionalHubbard model. The inclusion of the local dynamical vertex stemming from theDMFT self-energy and polarization is shown to cure the problems ofself-consistent GW in the description of spectral properties. We calculate themomentum-resolved spectral functions, the two-particle polarization andelectron loss spectra, and show that the inclusion of GW in extended DMFT leadsto a narrowing of the quasi-particle width and more pronounced Hubbard bands inthe metallic regime as one approaches the charge-ordering transition. Finally,the momentum-dependence introduced by GW into the extended DMFT description ofcollective modes is found to affect their shape, giving rise to dispersiveplasmon-like long-wavelength and stripe modes.

Spectral Properties of Correlated Materials: Local Vertex and Non-Local Two-Particle Correlations from Combined GW and Dynamical Mean Field Theory