1. Applications of DMFT to correlated electrons.
G. Kotliar
Physics Department and
Center for Materials Theory
Rutgers University

2. THE STATE UNIVERSITY OF NEW JERSEY
Outline
Introduction to the strong correlation problem.
Essentials of DMFT
Applications to the Mott transition problem: some insights from studies of models.
Towards an electronic structure method: applications to materials.
Outlook
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3. The electron in a solid: wave picture
Momentum Space , bands, k in Brillouin zone is good quantum number.
Maximum metallic resistivity 200 mohm cm
See if I still have bands in ens talk.
Landau Fermi liquid theory interactions renormalize away at low energy, simple band picture in effective field holds.
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4. Standard Model of Solids
Qualitative predictions: low temperature dependence of thermodynamics and transport.
Optical response, transitions between bands.
Qualitative predictions: filled bands give rise to insulting behavior. Compounds with odd number of electrons are metals.
Quantitative tools: Density Functional Theory with approximations suggested by the Kohn Sham formulation, (LDA GGA) is a successful computational tool for the total energy. Good starting point for perturbative calculation of spectra,eg. GW. Kinetic equations yield transport coefficients.
Put the qualitative idea of dft, functional of a density. Stress the power and the accuracy.
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5. Success story : Density Functional Linear Response
Tremendous progress in ab initio modelling of lattice dynamics
& electron-phonon interactions has been achieved
(Review: Baroni et.al, Rev. Mod. Phys, 73, 515, 2001)
(Savrasov, PRB 1996)

6. The electron in a solid: particle picture.
NiO, MnO, …Array of atoms is insulating if a>>aB. Mott: correlations localize the electron
e_ e_ e_ e_
Superexchange
Add a better picture of hydrogen atoms. See Motts book.
Think in real space , solid collection of atoms
High T : local moments, Low T spin-orbital order
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7. Mott : Correlations localize the electron
Low densities, electron behaves as a particle,use atomic physics, real space
One particle excitations: Hubbard Atoms: sharp excitation lines corresponding to adding or removing electrons. In solids they broaden by their incoherent motion, Hubbard bands (eg. bandsNiO, CoO MnO….)
H H H+ H H H motion of H+ forms the lower Hubbard band
H H H H- H H motion of H_ forms the upper Hubbard band
Quantitative calculations of Hubbard bands and exchange constants, LDA+ U, Hartree Fock. Atomic Physics.
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8. Localization vs Delocalization Strong Correlation Problem
A large number of compounds with electrons in partially filled shells, are not close to the well understood limits (localized or itinerant). Non perturbative problem.
These systems display anomalous behavior (departure from the standard model of solids).
Neither LDA or LDA+U or Hartree Fock work well.
Dynamical Mean Field Theory: Simplest approach to electronic structure, which interpolates correctly between atoms and bands. Treats QP bands and Hubbard bands.
Limits do not match except for the case that we have filled atomic shells
In which case band theory solve the problem.
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9. Strong correlation anomalies
Metals with resistivities which exceed the Mott Ioffe Reggel limit.
Transfer of spectral weight which is non local in frequency.
Dramatic failure of DFT based approximations in predicting physical properties.
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10. Correlated Materials do big things
Huge resistivity changes V2O3.
Copper Oxides. .(La2-x Bax) CuO4 High Temperature Superconductivity.150 K in the Ca2Ba2Cu3HgO8 .
Uranium and Cerium Based Compounds. Heavy Fermion Systems,CeCu6,m*/m=1000
(La1-xSrx)MnO3 Colossal Magneto-resistance.
Put some materials formulae for quaternary
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11. Strongly Correlated Materials.
Large thermoelectric response in CeFe4 P12 (H. Sato et al. cond-mat ). Ando et.al. NaCo2-xCuxO4 Phys. Rev. B 60, (1999).
Huge volume collapses, Ce, Pu……
Large and ultrafast optical nonlinearities Sr2CuO3 (T Ogasawara et.a Phys. Rev. Lett. 85, 2204 (2000) )
Get tokura osgawara PRL, and the science express, and ando prl , and formula units. Theory will play an important role in optimizing their physical properties
Ando et. Al. Phys. Rev. B 60, (1999).
Ogasawara Phys. Rev. Lett. 85, 2204 (2000)
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12. THE STATE UNIVERSITY OF NEW JERSEY
The Mott transition
Electronically driven MIT.
Forces to face the localization delocalization problem.
Relevant to many systems, eg V2O3
Techniques applicable to a very broad
range or problems.
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13. THE STATE UNIVERSITY OF NEW JERSEY
Mott transition in V2O3 under pressure or chemical substitution on V-site
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14. THE STATE UNIVERSITY OF NEW JERSEY
Universal and non universal features. Top to bottom approach to correlated materials.
Some aspects at high temperatures, depend weakly on the material (and on the model).
Low temperature phase diagram, is very sensitive to details, in experiment (and in the theory).
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15. THE STATE UNIVERSITY OF NEW JERSEY
Mott transition in layered organic conductors S Lefebvre et al. cond-mat/ , Phys. Rev. Lett. 85, 5420 (2000)
Update reference Phys. Rev. Lett. 85, 5420 (2000)
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16. Failure of the Standard Model: NiSe2-xSx
Miyasaka and Takagi (2000)
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17. THE STATE UNIVERSITY OF NEW JERSEY
Phase Diagrams :V2O3, Ni Se2-x Sx Mc Whan et. Al 1971,. Czek et. al. J. Mag. Mag. Mat. 3, 58 (1976),
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18. THE STATE UNIVERSITY OF NEW JERSEY
Outline
Introduction to the strong correlation problem and to the Mott transition.
Summary of the essential concepts of DMFT
Applications to the Mott transition problem: some insights from studies of models.
Towards an electronic structure method: applications to materials: Pu, Fe, Ni, LaSrTiO3, NiO,………….
Outlook
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19. Mean-Field : Classical vs Quantum
Classical case
Quantum case
Animate, and expand.
A. Georges, G. Kotliar (1992)
Phys. Rev. B 45, 6497
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20. Solving the DMFT equations
Wide variety of computational tools (QMC,ED….)Analytical Methods
Extension to ordered states.
Review: A. Georges, G. Kotliar, W. Krauth and M. Rozenberg Rev. Mod. Phys. 68,13 (1996)]
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21. THE STATE UNIVERSITY OF NEW JERSEY
DMFT: Effective Action point of view. R. Chitra and G. Kotliar Phys Rev. B. (2000).
Identify observable, A. Construct an exact functional of <A>=a, G [a] which is stationary at the physical value of a.
Example, density in DFT theory. (Fukuda et. al.)
When a is local, it gives an exact mapping onto a local problem, defines a Weiss field.
The method is useful when practical and accurate approximations to the exact functional exist. Example: LDA, GGA, in DFT.
It is useful to introduce a Lagrange multiplier l conjugate to a, G [a, l ].
It gives as a byproduct a additional lattice information.
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22. Example: DMFT for lattice model (e.g. single band Hubbard).
Observable: Local Greens function Gii (w).
Exact functional G [Gii (w) ].
DMFT Approximation to the functional.
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23. THE STATE UNIVERSITY OF NEW JERSEY
Extensions of DMFT.
Renormalizing the quartic term in the local impurity action.
EDMFT.
Taking several sites (clusters) as local entity.
CDMFT
Combining DMFT with other methods.
LDA+DMFT, GWU.
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24. THE STATE UNIVERSITY OF NEW JERSEY
Outline
Introduction to the strong correlation problem.
Essentials of DMFT
Applications to the Mott transition problem: some insights from studies of models.
Towards an electronic structure method: applications to materials: Pu, Fe, Ni, LaSrTiO3, NiO………….
Outlook
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25. Schematic DMFT phase diagram Hubbard model (partial frustration)
M. Rozenberg G. Kotliar H. Kajueter G Thomas D. Rapkine J Honig and P Metcalf Phys. Rev. Lett. 75, 105 (1995)
Hydrogen atom of strong correlation problme.
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26. THE STATE UNIVERSITY OF NEW JERSEY
Schematic DMFT phase diagram one band Hubbard model (half filling, semicircular DOS, partial frustration) Rozenberg et.al PRL (1995)
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27. THE STATE UNIVERSITY OF NEW JERSEY
Spectral Evolution at T=0 half filling full frustration. Three peak structure.
X.Zhang M. Rozenberg G. Kotliar (PRL 1993)
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28. Evolution of the Spectral Function with Temperature
Anomalous transfer of spectral weight connected to the proximity to the Ising Mott endpoint (Kotliar Lange and Rozenberg Phys. Rev. Lett. 84, 5180 (2000)
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29. THE STATE UNIVERSITY OF NEW JERSEY
Insights from DMFT
The Mott transition is driven by transfer of spectral weight from low to high energy as we approach the localized phase
Control parameters: doping, temperature,pressure…
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30. Parallel development: Fujimori et.al
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31. THE STATE UNIVERSITY OF NEW JERSEY
Mott transition in V2O3 under pressure or chemical substitution on V-site
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32. Anomalous transfer of optical spectral weight V2O3
:M Rozenberg G. Kotliar and H. Kajuter Phys. Rev. B 54, 8452 (1996).
M. Rozenberg G. Kotliar H. Kajueter G Tahomas D. Rapkikne J Honig and P Metcalf Phys. Rev. Lett. 75, 105 (1995)
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33. Anomalous transfer of spectral weight in v2O3
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34. Anomalous transfer of spectral weight in v2O3
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35. Anomalous Spectral Weight Transfer: Optics
Below energy
ApreciableT dependence found.
Schlesinger et.al (FeSi) PRL 71 ,1748 , (1993) B Bucher et.al. Ce2Bi4Pt3PRL 72, 522 (1994), Rozenberg et.al. PRB 54, 8452, (1996).
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36. THE STATE UNIVERSITY OF NEW JERSEY
ARPES measurements on NiS2-xSex Matsuura et. al Phys. Rev B 58 (1998) Doniach and Watanabe Phys. Rev. B 57, 3829 (1998) .
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37. THE STATE UNIVERSITY OF NEW JERSEY
Anomalous transfer of optical spectral weight, NiSeS. [Miyasaka and Takagi]
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38. Anomalous Resistivity and Mott transition Ni Se2-x Sx
Insights from DMFT: think in term of spectral
functions (branch cuts) instead of well defined
QP (poles )
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39. THE STATE UNIVERSITY OF NEW JERSEY
Qualitative phase diagram in the U, T , m plane (two band Kotliar Murthy Rozenberg PRL. Phys. Rev. Lett. 89, (2002)
Coexistence regions between localized and delocalized spectral functions.
k diverges at generic Mott endpoints
Boundary in beyond which perturbation theory stops working.
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40. THE STATE UNIVERSITY OF NEW JERSEY
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41. THE STATE UNIVERSITY OF NEW JERSEY
Ultrasound study of
Fournier et. al. (2002)
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42. Minimum of the melting point
Divergence of the compressibility at the Mott transition endpoint.
Rapid variation of the density of the solid as a function of pressure, in the localization delocalization crossover region.
Slow variation of the volume as a function of pressure in the liquid phase
Elastic anomalies, more pronounced with orbital degeneracy.
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43. THE STATE UNIVERSITY OF NEW JERSEY
Minimum in melting curve and divergence of the compressibility at the Mott endpoint
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44. THE STATE UNIVERSITY OF NEW JERSEY
Cerium
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45. Generalized phase diagramT
U/W
Structure, bands, orbitals
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46. THE STATE UNIVERSITY OF NEW JERSEY
Case study in f electrons, Mott transition in the actinide series. B. Johanssen 1974 Smith and Kmetko Phase Diagram 1984.
f electrons in Th Pr U Np are itinerant . From Am on they are localized. Pu is at the boundary.
Pu has a simple cubic fcc structure,the d phase which is easily stabilized over a wide region in the T,p phase diagram.
The d phase is non magnetic.
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47. Conclusions: generic aspects
Three peak structure, quasiparticles and Hubbard bands.
Non local transfer of spectral weight.
Large resistivities.
Finite temperature divergence of the compressibility.
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48. THE STATE UNIVERSITY OF NEW JERSEY
Insights from DMFT
Mott transition as a bifurcation of an effective action
Important role of the incoherent part of the spectral function at finite temperature
Physics is governed by the transfer of spectral weight from the coherent to the incoherent part of the spectra. Real and momentum space pictures are needed as synthesized in DMFT.
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49. THE STATE UNIVERSITY OF NEW JERSEY
Outline
Introduction to the strong correlation problem.
Essentials of DMFT
Applications to the Mott transition problem: some insights from studies of models.
Towards an electronic structure method: applications to materials
Outlook
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50. Interface DMFT with electronic structure.
Derive model Hamiltonians, solve by DMFT
(or cluster extensions). Total energy?
Full many body aproach, treat light electrons by GW or screened HF, heavy electrons by DMFT . Combining EDMFT with GW. Ping Sun and Phys. Rev. B 66, (2002). G.  Kotliar and S. Savrasov in New Theoretical Approaches to Strongly Correlated Systems, A. M. Tsvelik Ed Kluwer Academic Publishers cond-mat/
Treat correlated electrons with DMFT and light electrons with DFT (LDA, GGA +DMFT)
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51. THE STATE UNIVERSITY OF NEW JERSEY
Combining LDA and DMFT
The light, SP electrons well described by LDA. The heavier D electrons treat by DMFT.
LDA already contains an average interaction of the heavy electrons, subtract this out by shifting the heavy level (double counting term, Edc , review Anismov Aersetiwan and Lichtenstein )
Atomic physics parameters . U=F0 cost of double occupancy irrespectively of spin, J=F2+F4, Hunds energy favoring spin polarization , F2/F4=.6,…..
Calculations of U, Edc, (Gunnarson and Anisimov, Mc Mahan et.al. Hybertsen et.al) or viewed as parameters
Philosophy of the approach. Qualitative features of the results do not depend
In a sensitive way fon this choice.
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52. THE STATE UNIVERSITY OF NEW JERSEY
Spectral Density Functional : effective action construction (Fukuda, Valiev and Fernando , Chitra and GK).
Introduce local orbitals, caR(r-R)orbitals, and local GF
G(R,R)(i w) =
The exact free energy can be expressed as a functional of the local Greens function and of the density by introducing sources for r(r) and G and performing a Legendre transformation, G[r(r),G(R,R)(iw)]
Approximate functional using DMFT insights.
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53. LDA+DMFT Self-Consistency loopU
DMFT
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54. F Sum of local 2PI graphs with local U matrix and local G
LSDA+DMFT functional
F Sum of local 2PI graphs with local U matrix and local G
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55. Very Partial list of application of realistic DMFT to materials
QP bands in ruthenides: A. Liebsch et al (PRL 2000)
N phase of Pu: S. Savrasov et al (Nature 2001)
MIT in V2O3: K. Held et al (PRL 2001)
Magnetism of Fe, Ni: A. Lichtenstein et al PRL (2001)
J-G transition in Ce: K. Held et al (PRL 2000); M. Zolfl et al PRL (2000).
3d doped Mott insulator La1-xSrxTiO3 (Anisimov et.al 1997, Nekrasov et.al. 1999, Udovenko et.al 2002)
Paramagnetic Mott insulators. NiO MnO, Savrasov et. al.
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56. THE STATE UNIVERSITY OF NEW JERSEY
Functional approach allows computation of linear response.(S. Savrasov and GK 2002)
Apply to NiO, canonical Mott insulator.
U=8 ev, J=.9ev
Simple Impurity solver Hubbard 1.
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57. DMFT Results for NiO: Phonons
Solid circles – theory, open circles – exp. (Roy et.al, 1976)
DMFT

58. DMFT for Mott insulators
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59. THE STATE UNIVERSITY OF NEW JERSEY
Case study Fe and Ni
Archetypical itinerant ferromagnets
LSDA predicts correct low T moment
Band picture holds at low T
Main puzzle: at high temperatures c has a Curie Weiss law with a moment larger than the ordered moment.
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60. THE STATE UNIVERSITY OF NEW JERSEY
Iron and Nickel: crossover to a real space picture at high T (Lichtenstein, Katsnelson and Kotliar Phys Rev. Lett 87, , 2001)
Short Reference to PRL.
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61. THE STATE UNIVERSITY OF NEW JERSEY
Iron and Nickel:magnetic properties (Lichtenstein, Katsenelson,GK PRL 01)
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62. THE STATE UNIVERSITY OF NEW JERSEY
Ni and Fe: theory vs exp
meff / mB high T moment
Fe 3.1 (theory) 3.12 (expt)
Ni 1.5 (theory) (expt)
Curie Temperature Tc
Fe ( theory) (expt)
Ni (theory) (expt)
Short Bcc iron expt spin wave stiffness 314 mev/A^2
Fcc ni expt spin wave, 550 mev/A^2
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63. THE STATE UNIVERSITY OF NEW JERSEY
Fe and Ni
Consistent picture of Fe (more localized) and Ni
(more correlated)
Satellite in minority band at 6 ev, 30 % reduction of bandwidth, exchange splitting reduction .3 ev
Spin wave stiffness controls the effects of spatial flucuations, it is about twice as large in Ni and in Fe
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64. THE STATE UNIVERSITY OF NEW JERSEY
Photoemission Spectra and Spin Autocorrelation: Fe (U=2, J=.9ev,T/Tc=.8) (Lichtenstein, Katsenelson,Kotliar Phys Rev. Lett 87, , 2001)
Put correct reference
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65. Photoemission and T/Tc=.8 Spin Autocorrelation: Ni (U=3, J=.9 ev)
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66. THE STATE UNIVERSITY OF NEW JERSEY
Outline
Introduction to the strong correlation problem.
Essentials of DMFT
Applications to the Mott transition problem: some insights from studies of models.
Towards an electronic structure method: applications to materials: Pu, Fe, Ni, LaSrTiO3, NiO………….
Outlook
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67. THE STATE UNIVERSITY OF NEW JERSEY
Outlook
Local approach to strongly correlated electrons.
Many extensions, make the approach suitable for getting insights and quantitative results in correlated materials.
Field is in the early stages, applications so far have given very encouraging results.
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68. THE STATE UNIVERSITY OF NEW JERSEY
Phonons NiO
LDA
LSDA
LSDA+U
DMFT
Expt.
wTO Thz
wLO Thz e0
Egap
|Z*|
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69. THE STATE UNIVERSITY OF NEW JERSEY
Phonons MnO
LDA
LSDA
LSDA+U
DMFT
Expt.
wTO Thz
wLO Thz e0
Egap
|Z*|
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70. Acknowledgements: Development of DMFT
Collaborators: V. Anisimov, R. Chitra, V. Dobrosavlevic, D. Fisher, A. Georges, H. Kajueter, W.Krauth, E. Lange, A. Lichtenstein, G. Moeller, Y. Motome, G. Palsson, M. Rozenberg, S. Savrasov, Q. Si, V. Udovenko, X.Y. Zhang
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71. THE STATE UNIVERSITY OF NEW JERSEY
E-DMFT references
H. Kajueter and G. Kotliar (unpublished and Kajuter’s Ph.D thesis (1995)).
Q. Si and J L Smith PRL 77 (1996)3391 .
R. Chitra and G.Kotliar Phys. Rev. Lett 84, (2000 )
Y. Motome and G. Kotliar. PRB 62, (2000)
R. Chitra and G. Kotliar Phys. Rev. B 63, (2001)
S. Pankov and G. Kotliar PRB 66, (2002)
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72. DMFT Impurity cavity construction
animate
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73. Cluster extensions of DMFT
Two impurity method. [A. Georges and G. Kotliar (1995 unpublished ) and RMP 68,13 (1996) , A. Schiller PRL75, 113 (1995)]
M. Jarrell et al Dynamical Cluster Approximation [Phys. Rev. B ]
Periodic cluster] M. Katsenelson and A. Lichtenstein PRB 62, 9283 (2000).
G. Kotliar S. Savrasov G. Palsson and G. Biroli Cellular DMFT [PRL87, ]
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74. THE STATE UNIVERSITY OF NEW JERSEY
C-DMFT
C:DMFT The lattice self energy is inferred
from the cluster self energy.
Alternative approaches DCA (Jarrell et.al.) Periodic clusters (Lichtenstein and Katsnelson)
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75. C-DMFT: test in one dimension. (Bolech, Kancharla GK cond-mat 2002)
Gap vs U, Exact solution Lieb and Wu, Ovshinikov
Nc=2 CDMFT
vs Nc=1
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76. DMFT plus other methods.
DMFT+ LDA , V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, (1997).
A Lichtenstein and M. Katsenelson Phys. Rev. B 57, 6884 (1988).
S. Savrasov and G.Kotliar, funcional formulation for full self consistent implementation. Savasov Kotliar and Abrahams . Application to delta Pu Nature (2001)
Combining EDMFT with GW. Ping Sun and Phys. Rev. B 66, (2002). G.  Kotliar and S. Savrasov in New Theoretical Approaches to Strongly Correlated Systems, A. M. Tsvelik Ed Kluwer Academic Publishers cond-mat/
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77. Limit of large lattice coordination
Metzner Vollhardt, 89
Muller-Hartmann 89
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78. THE STATE UNIVERSITY OF NEW JERSEY
ARPES measurements on NiS2-xSex Matsuura et. Al Phys. Rev B 58 (1998) Doniaach and Watanabe Phys. Rev. B 57, 3829 (1998) .
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79. THE STATE UNIVERSITY OF NEW JERSEY
LaxSr1-x TiO3
Adding holes to a Mott insulator in three dimensions.
Canonical example of a Brinkman Rice system.
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80. (Tokura et. Al. 1993)A doped Mott insulator:LaxSr1-xO3
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81. DMFT calculation U near the Mott transition, Rozenberg et.al 94
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82. Hall Coefficient, electron like.
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83. La1-xSrxTiO3 photoemission
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84. Evolution of spectra with doping U=4
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85. THE STATE UNIVERSITY OF NEW JERSEY
Optical conductivity
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86. Realistic Computation of Optical Properties : La1-xSrxTiO3
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87. Optical spectral weight
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88. THE STATE UNIVERSITY OF NEW JERSEY
Resistivities
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89. THE STATE UNIVERSITY OF NEW JERSEY
Resistivities
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90. THE STATE UNIVERSITY OF NEW JERSEY
LiVO4
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91. THE STATE UNIVERSITY OF NEW JERSEY
Thermodynamics LiVO4
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92. Resistivity saturation
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93. Anomalous Resistivities: Doped Hubbard Model G. Palsson 1998
NCA
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94. Anomalous Resistivities: Doped Hubbard Model (QMC)
Prushke and Jarrell 1993
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95. THE STATE UNIVERSITY OF NEW JERSEY
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96. THE STATE UNIVERSITY OF NEW JERSEY
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97. THE STATE UNIVERSITY OF NEW JERSEY
Functional approach allows computation of linear response.(S. Savrasov and GK 2002)
Apply to NiO, canonical Mott insulator.
U=8 ev, J=.9ev
Simple Impurity solver Hubbard 1.
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RUTGERS

98. DMFT for Mott insulators
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RUTGERS

99. DMFT Results for NiO: Phonons
Solid circles – theory, open circles – exp. (Roy et.al, 1976)
DMFT

100. THE STATE UNIVERSITY OF NEW JERSEY
Phonons NiO
LDA
LSDA
LSDA+U
DMFT
Expt.
wTO Thz
wLO Thz e0
Egap
|Z*|
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RUTGERS

101. THE STATE UNIVERSITY OF NEW JERSEY
Phonons MnO
LDA
LSDA
LSDA+U
DMFT
Expt.
wTO Thz
wLO Thz e0
Egap
|Z*|
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RUTGERS

102. LDA+DMFT Self-Consistency loopU
DMFT
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RUTGERS

103. THE STATE UNIVERSITY OF NEW JERSEY
Ni and Fe: theory vs exp
m( T=.9 Tc)/ mB ordered moment
Fe ( theory) (expt)
Ni (theory) (expt)
meff / mB high T moment
Fe 3.1 (theory) 3.12 (expt)
Ni 1.5 (theory) (expt)
Curie Temperature Tc
Fe ( theory) (expt)
Ni (theory) (expt)
Short Bcc iron expt spin wave stiffness 314 mev/A^2
Fcc ni expt spin wave, 550 mev/A^2
Expt .9tc 1.55 fe otc 2.2 ratio .7
Expt .9tc .35 ni t=0 .6 ratio .58
Multiply by get 2.5 theory vs 2.2 expt
And vs .6
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RUTGERS

104. Kohn Sham reference system
Excellent starting point for computation of spectra in perturbation theory in screened Coulomb interaction GW.
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RUTGERS

105. LDA+DMFT Self-Consistency loopU
DMFT
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RUTGERS

106. F Sum of local 2PI graphs with local U matrix and local G
LDA+DMFT functional
F Sum of local 2PI graphs with local U matrix and local G
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RUTGERS

107. F Sum of local 2PI graphs with local U matrix and local G
LSDA+DMFT functional
F Sum of local 2PI graphs with local U matrix and local G
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RUTGERS

108. F Sum of local 2PI graphs with local U matrix and local G
LDA+DMFT functional
F Sum of local 2PI graphs with local U matrix and local G
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RUTGERS

109. THE STATE UNIVERSITY OF NEW JERSEY
Comments on LDA+DMFT
Static limit of the LDA+DMFT functional , with F= FHF reduces to LDA+U
Removes inconsistencies of this approach,
Only in the orbitally ordered Hartree Fock limit, the Greens function of the heavy electrons is fully coherent
Gives the local spectra and the total energy simultaneously, treating QP and H bands on the same footing.
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110. THE STATE UNIVERSITY OF NEW JERSEY
LDA+U
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RUTGERS

111. LDA+DMFT Connection with atomic limit
Weiss field
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RUTGERS