Methods
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Dynamical mean-field theory
Dynamical mean-field theory is the excellent approach for studying strong electronic correlations in various systems. It is described in detail in
A. Georges, G. Kotliar, W. Krauth, and M. Rozenberg, Rev. Mod. Phys. 68, 13 (1996);
G. Kotliar and D. Vollhardt, Physics Today 57 (3), 53 (2004).
For solution of the impurity problem of DMFT I use the following tools:
Papers
Papers
1. Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory, G. Rohringer, H. Hafermann, A. Toschi, A. A. Katanin, A. E. Antipov, M. I. Katsnelson, A. I. Lichtenstein, A. N. Rubtsov, K. Held, Rev. Mod. Phys. 90, 025003 (2018)
2. One-particle irreducible functional approach - a new route to diagrammatic extensions of DMFT, G. Rohringer, A. Toschi, H. Hafermann, K. Held, V.I. Anisimov, A. A. Katanin, Phys. Rev. B 88, 115112 (2013)
3. The effect of six-point one-particle reducible local interactions in the dual fermion approach. A. A. Katanin, J. Phys. A: Math. Theor. 46, 045002 (2013).
4. «Dynamical vertex approximation - an introduction», K. Held, A. A. Katanin, A. Toschi, Progr. Theor. Phys. Suppl. 176, 117 (2008).
5. «Dynamical vertex approximation – a step beyond dynamical mean field theory», A. Toschi, A. A. Katanin, and K. Held, Phys. Rev. B 75, 045118 (2007).
6. «Comparing pertinent effects of antiferromagnetic fluctuations in the two and three dimensional Hubbard model», A. A. Katanin, A. Toschi, K. Held, Phys. Rev. B 80, 075104 (2009).
Functional renormalization group
This method is used to describe accurately non-local correlations in bosonic and fermionic systems. My own (with coauthors) developments in these field are listed in the "Papers" below.
Papers
Papers
1. Functional renormalization-group approaches, one-particle (ir)reducible with respect to local Green functions, using the dynamical mean-field theory as a starting point, A. A. Katanin, JETP 120, 1085 (2015)
2. Correlated starting points for the functional renormalization group, N. Wentzell, C. Taranto, A. A. Katanin, A. Toschi, S. Andergassen, Phys. Rev. B 91, 045120 (2015)
3. From infinite to two dimensions through the functional renormalization group, C. Taranto, S. Andergassen, J. Bauer, K. Held, A. Katanin, W. Metzner, G. Rohringer, A. Toschi, Phys. Rev. Lett. 112, 196402 (2014)
4. «Self-energy effects in the Polchinski and Wick-ordered renormalization-group approaches», A. A. Katanin, J. Phys. A 44, 495004 (2011).
5. «The two-loop functional renormalization group approach to the one- and two-dimensional Hubbard model», A. A. Katanin, Phys. Rev. B 79, 235119 (2009).
6. «Renormalization group for phases with broken discrete symmetry near quantum critical points», P. Jakubczyk, P. Strack, A. A. Katanin, and W. Metzner, Phys. Rev. B 77, 195120 (2008).
7. «On the fulfillment of Ward identities in the functional renormalization group approach», A.A. Katanin, Phys. Rev. B 70, 115109 (2004).
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