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Quantum many-body theory at the two-particle level: Challenges and new perspectives

Alessandro Toschi, Vienna University

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 [3]. Furthermore, it allows to study non-local correlations on all length-scales through diagrammatic extensions of DMFT [4], as the dynamical vertex approximation (DΓA)[5]. 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 [6]. Such an enhanced physical understanding has also called for a correspondingly improved algorithmic treatment [2] 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 .

[1] G. Rohringer, A. Valli, and A. Toschi, PRB 86, 125114 (2012); T. Schäfer, et al., PRL 110, 246405 (2013).
[2] N. Wentzell et al., arXiv:1610.06520.
[3] G. Rohringer et al., arXiv:1705.00024, submitted to RMP
[4] A. Toschi, et al., PRB 86, 064411 (2012).
[5] A. Toschi, A. A. Katanin, and K. Held, PRB 75 045118 (2007).
[6] T Schäfer, et al., PRB 91, 125109 (2015); G. Rohringer, et al., PRL 107, 256402 (2011); T. Schäfer, et al., arXiv.
[7] N. Wentzell, et al. PRB 91, 115115 (2015).

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