https://hal-cea.archives-ouvertes.fr/cea-01341620v2Ayral, ThomasThomasAyralIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueParcollet, OlivierOlivierParcolletIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueMott physics and collective modes: an atomic approximation of the four-particle irreducible functionalHAL CCSD2016cond-mat[PHYS] Physics [physics]Savelli, BrunoQuantitative approaches for strongly correlated quantum systems in equilibrium and far from equilibrium. - MOTTMETALS - - EC:FP7:ERC2012-01-01 - 2017-12-31 - 278472 - VALID - 2022-10-03 15:53:312022-10-05 03:29:502022-10-03 16:00:31enJournal articleshttps://hal-cea.archives-ouvertes.fr/cea-01341620v2/document10.1103/PhysRevB.94.075159https://hal-cea.archives-ouvertes.fr/cea-01341620v1application/pdf2We discuss a generalization of the dynamical mean field theory (DMFT) for strongly correlated systems close to a Mott transition based on a systematic approximation of the fully irreducible four-point vertex. It is an atomic-limit approximation of a functional of the one- and two-particle Green functions, built with the second Legendre transform of the free energy with respect to the two-particle Green function. This functional is represented diagrammatically by four-particle irreducible (4PI) diagrams. Like the dynamical vertex approximation (D$\Gamma$A), the fully irreducible vertex is computed from a quantum impurity model whose bath is self-consistently determined by solving the parquet equations. However, in contrast with D$\Gamma$A and DMFT, the interaction term of the impurity model is also self-consistently determined. The method interpolates between the parquet approximation at weak coupling and the atomic limit, where it is exact. It is applicable to systems with short-range and long-range interactions.