Prologue to Dynamical Mean Field Theory DMFT and its Applications to the Electronic Structure of Correlated Materi .


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References. Electronic structure figurings with dynamical mean-field hypothesis: G. Kotliar, S.
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Prologue to Dynamical Mean Field Theory (DMFT) and its Applications to the Electronic Structure of Correlated Materials G.Kotliar Physics Department Center for Materials Theory Rutgers University. Zacatecas Mexico PASSI School . Montauk June (2006). Partners: K. Haule (Rutgers), C. Marianetti (Rutgers ) S. Savrasov (UC Davis)

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References Electronic structure estimations with dynamical mean-field hypothesis: G. Kotliar, S. Savrasov, K. Haule, V. Oudovenko, O. Parcollet, and C. Marianetti, Rev. of Mod. Phys. 78, 000865 (2006). Dynamical Mean Field Theory of Strongly Correlation Fermion Systems and the Limit of Infinite Dimensions:  A. Georges, G. Kotliar, W. Krauth, and M. Rozenberg, Rev. of Mod. Phys. 68, 13-125 (1996) . Electronic Structure of Strongly Correlated Materials: Insights from Dynamical Mean Field Theory: Gabriel Kotliar and Dieter Vollhardt, Physics Today 57, 53 (2004).

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What is a firmly related material ?

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Electrons in a Solid:the Standard Model Band Theory: electrons as waves. Landau Fermi Liquid Theory. n band list, e.g. s, p, d,,f Rigid groups , optical moves , thermodynamics, transport… … Quantitative Tools. Thickness Functional Theory Kohn Sham (1964) Static Mean Field Theory. Kohn Sham Eigenvalues and Eigensates: Excellent beginning stage for irritation hypothesis in the screened collaborations (Hedin 1965) 2

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Success story : Density Functional Linear Response Tremendous advance in abdominal muscle initio demonstrating of grid flow & electron-phonon connections has been accomplished ( Review: Baroni et.al, Rev. Mod. Phys, 73 , 515, 2001 ) ( Savrasov, PRB 1996 )

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Kohn Sham reference framework Excellent beginning stage for calculation of spectra in annoyance hypothesis in screened Coulomb cooperation GW.

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- [ - ] = [ - ] - 1 = G = W GW estimate (Hedin )

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Kohn Sham Eigenvalues and Eigensates: Excellent beginning stage for bother hypothesis in the screened associations (Hedin 1965) Self Energy VanShilfgaarde (2005) 3

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Strong Correlation Problem:where the standard model comes up short Fermi Liquid Theory works yet parameters can\'t be registered in annoyance hypothesis. Fermi Liquid Theory does NOT work . Require new ideas to supplant of unbending groups ! Incompletely filled d and f shells. Rivalry amongst active and Coulomb collaborations. Breakdown of the wave picture. Need to join a genuine space point of view (Mott). Non perturbative issue. 4

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Localization versus Delocalization Strong Correlation Problem A substantial number of mixes with electrons in incompletely filled shells, are not near the surely knew limits (completely restricted or completely vagrant). Circumstance acknowledged by applying a control parameters, e.g. weight. Metal to Insulator Transition. A few materials have a few types of electrons, some confined (f \'s d\'s ) some vagrant (sp, spd) . OSMT. Overwhelming Fermions. Presenting conveys (electrons or openings) to a Mott protector. Doping Driven Mott move.

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Why is it beneficial to concentrate corresponded electron materials ?

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Localization versus Delocalization Strong Correlation Problem A substantial number of mixes with electrons in mostly filled shells, are not near the surely knew limits (restricted or nomad). Non perturbative issue. These frameworks show peculiar conduct (takeoff from the standard model of solids). Neither LDA or LDA+U or Hartree Fock function admirably. Dynamical Mean Field Theory: Simplest way to deal with electronic structure, which inserts accurately amongst particles and groups. Treats QP groups and Hubbard groups.

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Strongly corresponded frameworks Copper Oxides. High Temperature Superconductivity . Cobaltates Anomalous thermoelectricity. Manganites . Giant magnetoresistance. Substantial Fermions. Tremendous quasiparticle masses. 2d Electron gasses. Metal to protector moves. Lanthanides, Transition Metal Oxides, Multiferroics… … .. 5

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Basic Questions How does the electron go from being limited to nomad. How do the physical properties advance. Step by step instructions to connect between the minute data (nuclear positions) and exploratory estimations. New ideas, new strategies

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How would we test SCES tentatively ?

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One Particle Spectral Function and Angle Integrated Photoemission e Probability of expelling an electron and transfering vitality w =Ei-Ef, and force k f( w ) A( w, K ) M 2 Probability of engrossing an electron and transfering vitality w =Ei-Ef, and energy k (1-f( w )) A( w K ) M 2 Theory. Register one molecule greens capacity and utilize otherworldly capacity. n e

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Spectral Function Photoemission and relationships e Probability of evacuating an electron and transfering vitality w =Ei-Ef, and force k f( w ) A( w, K ) M 2 Weak Correlation Strong Correlation n Angle coordinated unearthly capacity 8

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Strong Correlation Problem:where the standard model falls flat Fermi Liquid Theory works yet parameters can\'t be figured in annoyance hypothesis. Fermi Liquid Theory does NOT work . Require new ideas to supplant of unbending groups ! Incompletely filled d and f shells. Rivalry amongst active and Coulomb connections. Breakdown of the wave picture. Need to join a genuine space point of view (Mott). Non perturbative issue. 4

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How would we approach the issue of unequivocally corresponded electron stystems ?

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Two streets for stomach muscle initio estimation of electronic structure of firmly corresponded materials Crystal structure +Atomic positions Model Hamiltonian Correlation Functions Total Energies and so on

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Strongly related frameworks are normally treated with model Hamiltonians Tight restricting structure. Dispose of the "unimportant" high vitality degrees of opportunity Add powerful Coulomb association terms .

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One Band Hubbard show U/t Doping d or concoction potential Frustration (t\'/t) T temperature Mott move as a component of doping, weight temperature and so forth

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How would we lessen the many body issue to something tractable ?

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DMFT Cavity Construction. H appy marriage of nuclear and band material science. Extremize a useful of the nearby spectra. Nearby self vitality. Audits: A. Georges G. Kotliar W. Krauth and M. Rozenberg RMP68 , 13, 1996 Gabriel Kotliar and Dieter Vollhardt Physics Today 57,(2004). G. Kotliar S. Savrasov K. Haule V. Oudovenko O. Parcollet and C. Marianetti Rev. Mod. Phys. 78 , 865 (2006) . G. Kotliar and D . Vollhardt Physics 53 Today (2004)

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Mean-Field : Classical versus Quantum Classical case Quantum case A. Georges, G. Kotliar (1992) Phys. Rev. B 45, 6497

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Single site DMFT Impurity depression development: A. Georges, G. Kotliar, PRB, (1992)] Weiss field

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Extension to bunches. Cell DMFT. C-DMFT. G. Kotliar,S.Y. Savrasov, G. Palsson and G. Biroli, Phys. Rev. Lett. 87, 186401 (2001) tˆ(K) is the bouncing communicated in the superlattice documentations. Other group expansions (DCA, settled bunch plans, PCMDFT ), causality issues, O. Parcollet, G. Biroli and GK cond-matt 0307587 (2003)

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What is the structure of the DMFT issue ? Inserting and truncation

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Solving the DMFT conditions Wide assortment of computational instruments (QMC,ED… .)Analytical Methods Extension to requested states. Survey: A. Georges, G. Kotliar, W. Krauth and M. Rozenberg Rev. Mod. Phys. 68,13 (1996)]

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How would we sum up this development reasonable frameworks ?

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More broad DMFT circle

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Dynamical Mean Field Theory. Pit Construction. A. Georges and G. Kotliar PRB 45, 6479 (1992). A( w ) 10

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A( w ) A. Georges, G. Kotliar (1992) 11

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Dynamical Mean Field Theory Weiss field is a capacity. Various scales in unequivocally associated materials. Correct in the cutoff of substantial coordination (Metzner and Vollhardt 89) , active and collaboration vitality contend on equivalent balance. Prompt augmentation to genuine materials DFT+DMFT 12

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Evolution of the DOS. Hypothesis and investigations 13

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DMFT Qualitative Phase graph of a disappointed Hubbard demonstrate at whole number filling T/W 14

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T=170 T=300 Interaction with Experiments. Photoemission Three pinnacle strucure. V2O3:Anomalous exchange of ghastly weight M. Rozenberg G. Kotliar H. Kajueter G Thomas D. Rapkine J Honig and P Metcalf Phys. Rev. Lett. 75, 105 (1995) 15

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Photoemission estimations and Theory V2O3 Mo, Denlinger, Kim, Park, Allen, Sekiyama, Yamasaki, Kadono, Suga, Saitoh, Muro, Metcalf, Keller, Held, Eyert, Anisimov, Vollhardt PRL . (2003 ) . NiSxSe 1-x Matsuura Watanabe Kim Doniach Shen Thio Bennett (1998) Poteryaev et.al. (to be distributed) 16

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How would we settle the polluting influence demonstrate ?

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Methods of arrangement : a few illustrations Iterative annoyance hypothesis. A Georges and G Kotliar PRB 45, 6479 (1992). H Kajueter and G. Kotliar PRL (1996). Interpolative plans (Oudovenko et.al.) Exact diag plans Rozenberg et. al. PRL 72, 2761 (1994)Krauth and Caffarel. PRL 72, 1545 (1994) Projective strategy G Moeller et. al. PRL 74 2082 (1995). NRG R. Bulla PRL 83, 136 (1999)

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QMC M. Jarrell, PRL 69 (1992) 168, Rozenberg Zhang Kotliar PRL 69, 1236 (1992) ,A Georges and W Krauth PRL 69, 1240 (1992) M. Rozenberg PRB 55, 4855 (1987) . NCA Prushke et. al. (1993) . SUNCA K. Haule (2003). Logical methodologies, slave bosons. Scientific treatment close extraordinary focuses.

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How great is DMFT ?

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Single site DMFT is correct

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