Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials

Vollhardt, D.; Avella, Adolfo; Mancini, Ferdinando

doi:10.1063/1.3518901

Cited by 30 publications

(15 citation statements)

References 196 publications

(442 reference statements)

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“…The Hubbard Hamiltonian encodes a daunting competition between two energy scales [76][77][78]: the kinetic energy t, which measures the overlap between wave functions on neighboring lattice sites, and the interaction energy U > 0, which measures the strength of on-site repulsions. The single-band Fermi-Hubbard Hamiltonian reads:…”

Section: Hubbard Correlations and Split Bandsmentioning

confidence: 99%

Artificial honeycomb lattices for electrons, atoms and photons

et al. 2013

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Artificial honeycomb lattices offer a tunable platform to study massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on nanopatterning of two-dimensional electron gases in semiconductors, molecule-by-molecule assembly by scanning probe methods, and optical trapping of ultracold atoms in crystals of light. We also discuss photonic crystals with Dirac cone dispersion and topologically protected edge states. We emphasize how the interplay between single-particle band structure engineering and cooperative effects leads to spectacular manifestations in tunneling and optical spectroscopies.

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Section: Hubbard Correlations and Split Bandsmentioning

confidence: 99%

Artificial honeycomb lattices for electrons, atoms and photons

et al. 2013

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“…In contrast to DFT, huge progress has been made in describing strongly-correlated materials with dynamical mean-field theory (DMFT) [15][16][17][18][19][20]. DMFT is a sophisticated method which offers a higher level of theoretical description than DFT and bridges the gap between DFT and Green function approaches.…”

Section: Introductionmentioning

confidence: 99%

Many-body renormalization of forces in f -electron materials

et al. 2018

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Publisher's copyright statement:Reprinted with permission from the American Physical Society: Plekhanov, Evgeny, Hasnip, Phil, Sacksteder, Vincent, Probert, Matt, Clark, Stewart J., Refson, Keith Weber, Cedric (2018). Many-body renormalization of forces in f-electron materials. Physical Review B 98(7): 075129 c 2018 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We present the implementation of dynamical mean-field theory (DMFT) in the CASTEP ab initio code. We explain in detail the theoretical framework for DFT+DMFT and we demonstrate our implementation for three strongly-correlated systems with f -shell electrons: γ -cerium, cerium sesquioxide Ce 2 O 3 , and samarium telluride SmTe by using a Hubbard I solver. We find very good agreement with previous benchmark DFT+DMFT calculations of cerium compounds, while for SmTe we show the improved agreement with the experimental structural parameters as compared with LDA. Our implementation works equally well for both norm-conserving and ultrasoft pseudopotentials, and we apply it to the calculation of total energy, bulk modulus, equilibrium volumes, and internal forces in the two cerium compounds. In Ce 2 O 3 we report a dramatic reduction of the internal forces acting on coordinates not constrained by unit cell symmetries. This reduction is induced by the many-body effects, which can only be captured at the DMFT level. In addition, we derive an alternative form for treating the high-frequency tails of the Green function in Matsubara frequency summations. Our treatment allows a reduction in the bias when calculating the correlation energies and occupation matrices to high precision.

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“…Subsequently, Georges and Kotliar formulated the idea of mapping the Hubbard model in the infinite dimensional limit into a self consistent single site quantum impurity model, and hence laid the foundations of the dynamical mean field theory (DMFT) approach (31,12). This non-perturbative approach has directed towards significant advancement in understanding strongly correlated systems (18,7,12,32,33,9,31,34). DMFT can be considered as an analogue of a classical mean field theory for a ferromagnetic system: The classical and static mean field theory for the magnetic system introduces a magnetic field that is induced by the average magnetization of the whole crystal acting on each magnetic atom.…”

Section: Dynamical Mean Field Theorymentioning

confidence: 99%

Applications of DFT + DMFT in Materials Science

Paul

Birol

2019

Annu. Rev. Mater. Res.

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First principles methods can provide insight into materials that otherwise is impossible to acquire. Density Functional Theory (DFT) has been the first principles method of choice for numerous applications, but it falls short of predicting the properties of correlated materials. First principles Density Functional Theory + Dynamical Mean Field Theory (DFT+DMFT) is a powerful tool that can address these shortcomings of DFT when applied to correlated metals. In this brief review, which is aimed at non-experts, we review the basics and some applications of DFT+DMFT.

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Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials

Cited by 30 publications

References 196 publications

Artificial honeycomb lattices for electrons, atoms and photons

Artificial honeycomb lattices for electrons, atoms and photons

Many-body renormalization of forces in f -electron materials

Applications of DFT + DMFT in Materials Science

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