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Nonlocal Coulomb interactions and electronic correlations : novel many-body approaches

Thomas Ayral

Electronic correlations — the effect of local and nonlocal interactions between electrons in a system — raise deep challenges to theoretical physics. While dynamical mean field theory (DMFT) and its cluster extensions are best suited for handling strong local interactions and aptly describe the resulting local and short-ranged correlations, extensions are needed whenever nonlocal interactions impact the system’s properties, or when the feedback of nonlocal correlation effects beyond the cluster size due to local interactions needs to be taken into account.
In this presentation, I will focus on the two directions outlined above. I will start by showing that the self-consistent combination of extended DMFT (EDMFT) with the GW approximation (GW+EDMFT) yields valuable insights into charge-ordering phenomena in systems with nonlocal interactions [1,2]. I will focus on systems of ad-atoms on semiconducting surfaces, where the incorporation of long-ranged interactions allows to map out a coherent materials trend [3], and where the examination of the time- and momentum-resolved charge susceptibility gives a coherent account of apparent experimental contradictions in the Sn/Si compound [4].
I will then describe a new method which unifies the spin fluctuation and the Mott physics description of strongly-correlated materials. This method, dubbed ’TRILEX’, is based on a local approximation of the three-particle irreducible vertex function [5,6]. This vertex is self-consistently computed by solving a quantum impurity model with dynamical interactions in the charge and spin channels, using a continuous-time quantum Monte-Carlo algorithm. The electronic self-energy and the polarization constructed from this vertex are both frequency- and momentum- dependent. TRILEX incorporates, at a comparatively low computational expense, local correlations as well as feedback from some long-range spin and charge fluctuations. Upon doping, one finds a Fermi arc in the one-particle spectral function, which is one signature of the pseudo-gap state.
[1] TA, Philipp Werner, Silke Biermann, Phys. Rev. Lett. 109, 226401 (2012) [2] TA, Silke Biermann, Philipp Werner, Phys. Rev. B 87, 125149 (2013) [3] Philipp Hansmann, TA, Loïg Vaugier, Philipp Werner, Silke Biermann, Phys. Rev. Lett. 110, 166401 (2013) [4] Philipp Hansmann, TA, Antonio Tejeda, Silke Biermann, Scientific Reports 6, 19728 (2016) [5] TA, Olivier Parcollet, Phys. Rev. B. 92, 115 109 (2015) [6] TA, Olivier Parcollet, arXiv : 1512.06719

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