Cellular Dynamical Mean Field Approach to Strongly Correlated Systems

By Gabriel Kotliar, S. Savrasov, G. Pálsson. 2000

404 citations recorded by the source corpus.

We propose a cellular version of dynamical-mean field theory which gives a natural generalization of its original single-site construction and is formulated in different sets of variables. We show how non-orthogonality of the tight-binding basis sets enters the problem and prove that the resulting equations lead to manifestly causal self energies.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/8161f9693b031bd04173044a43c26bc29459fb3c

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model (2020, methodology): “[66] G.”
Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory (2017, background): “Particularly important and widely employed are cluster extensions of DMFT: the dynamical cluster approximation (DCA) by Hettler et al., 1998 and the cellular DMFT (CDMFT) by Lichtenstein and Katsnelson, 2000 and Kotliar et al., 2001.”
Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach (2016, background): “Hence in the following we review the main results for quantum quenches obtained by means of the Gutzwiller approximation and DMFT.”
Hubbard‐corrected DFT energy functionals: The LDA+U description of correlated systems (2013, background): “Other problematic aspects of DFT+DMFT are instead inherent to the approximations made in solving the Anderson impurity model such as, the finite sampling of the Greens functions on the frequency axis, the lack of self-consistency over the charge density, or the overlook of spatial fluctuations, some”
Electrodynamics of correlated electron materials (2011, background): “Since the low temperature monoclinic phase shows simultaneous Mott and Peierls correlations, the authors had to go beyond single site DMFT and include the tendency for dimerization by a cluster extension of DMFT (Kotliar et al., 2001).”
Electronic structure calculations with dynamical mean-field theory (2005, methodology): “The lattice Green’s function can then be reconstructed from the lattice cumulant Stanescu and Kotliar, 2005 or the lattice self-energy Kotliar et al., 2001; Biroli and Kotliar, 2002 , namely, G k , − t k + − k , −1 or G k , −t k +M k , −1 −1.”
Continuous-time Monte Carlo methods for quantum impurity models (2010, methodology): “We now turn to results relating to stronger coupling physics, beginning with results obtained for four site clusters, which have been studied using CDMFT (Kotliar et al., 2001) and DCA (Hettler et al., 1998) versions of cluster dynamical mean field theory.”
Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory (2015, methodology): “In a cluster mean-field approach embodied by cluster DMET (and similarly CDMFT) a concern is that the observation of local order in finite clusters does not translate into true long-range order.”
Quantum cluster theories (2004, methodology): “In this review we restrict the discussion to the usual, completely localized orthogonal basis set and refer the reader to Kotliar et al. (2001) for the generalization to arbitrary basis sets.”
Nonequilibrium dynamical mean-field theory and its applications (2013, methodology): “There are two well-established approaches to construct a cluster extension of DMFT, namely the cellular DMFT (Kotliar et al., 2001; Lichtenstein and Katsnelson, 2000) and the dynamical cluster approximation (DCA) (Hettler et al., 2000, 1998).”