Quantum many-body theory at the two-particle level: Challenges and new perspectives
31.05.2017 at 12:15
Our physical understanding is mostly based on the quantum many-body description at the one- or two-particle level. For strong correlations, the dynamical mean-field theory (DMFT), a self-consistent approach at the one-particle level, has represented a big step forward in the last two decades. Recently, however, the scientific frontier has moved to the treatment of correlations at the two-particle level[1,2]. Physically, this represents a key progress to understand spectroscopic experiments beyond photoemission . Furthermore, it allows to study non-local correlations on all length-scales through diagrammatic extensions of DMFT , as the dynamical vertex approximation (DΓA). By means of DΓA, the "fate" of the Mott-transition in 2D and the quantum critical exponents of the Hubbard model could be eventually calculated . Such an enhanced physical understanding has also called for a correspondingly improved algorithmic treatment  of the fully frequency and momentum dependent two-particle vertex functions, whose application is crucial in several [3,7] of the cutting-edge quantum many-body methods .
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 N. Wentzell, et al. PRB 91, 115115 (2015).
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