Electronic Structure of Strongly Correlated Materials a DMFT

  • Slides: 81
Download presentation
Electronic Structure of Strongly Correlated Materials : a DMFT Perspective Gabriel Kotliar Physics Department

Electronic Structure of Strongly Correlated Materials : a DMFT Perspective Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University Canada April 2002

Outline n n n Introduction to strongly correlated electrons Dynamical Mean Field Theory Model

Outline n n n Introduction to strongly correlated electrons Dynamical Mean Field Theory Model Hamiltonian Studies. Universal aspects insights from DMFT System specific studies: LDA+DMFT Outlook THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Strongly Correlated Materials n n n Copper Oxides. . (La 2 -x Bax) Cu.

Strongly Correlated Materials n n n Copper Oxides. . (La 2 -x Bax) Cu. O 4 High Temperature Superconductivity. 150 K in the Ca 2 Ba 2 Cu 3 Hg. O 8. Uranium and Cerium Based Compounds. Heavy Fermion Systems, Ce. Cu 6, m*/m=1000 (La 1 -x. Srx)Mn. O 3 Colossal Magneto-resistance. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Strongly Correlated Materials. n n n High Temperature Superconductivity in doped filled Bucky Balls

Strongly Correlated Materials. n n n High Temperature Superconductivity in doped filled Bucky Balls (J. H. Schon et. al Science Express 1064773 (2001)) CHBr 3 C 60 Tc=117 K. Large thermoelectric response in Ce. Fe 4 P 12 (H. Sato et al. cond-mat 0010017). Ando et. al. Na. Co 2 -x. Cux. O 4 Phys. Rev. B 60, 10580 (1999). Large and ultrafast optical nonlinearities Sr 2 Cu. O 3 (T Ogasawara et. a Phys. Rev. Lett. 85, 2204 (2000) ) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

The electron in a solid: wave picture Momentum Space (Sommerfeld) Maximum metallic resistivity 200

The electron in a solid: wave picture Momentum Space (Sommerfeld) Maximum metallic resistivity 200 mohm cm Standard model of solids (Bloch, Landau) Periodic potential, waves form bands , k in Brillouin zone. Interactions renormalize away. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Standard Model of Solids § § Qualitative predictions: low temperature dependence of thermodynamics and

Standard Model of Solids § § Qualitative predictions: low temperature dependence of thermodynamics and transport. Optical response, transition between the 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. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

The electron in a solid: particle picture. n Array of hydrogen atoms is insulating

The electron in a solid: particle picture. n Array of hydrogen atoms is insulating if a>>a. B. Mott: correlations localize the electron e_ e_ e_ Superexchange Think in real space , solid collection of atoms High T : local moments, Low T spin-orbital order THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Mott : Correlations localize the electron Low densities, electron behaves as a particle, use

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. bands. Ni. O, Co. O Mn. O…. ) H H H+ H H H- H H motion of H+ forms the lower Hubbard band motion of H_ forms the upper Hubbard band Quantitative calculations of Hubbard bands and exchange constants, LDA+ U, Hartree Fock. Atomic Physics. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Localization vs Delocalization Strong Correlation Problem • A large number of compounds with electrons

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 b and Hubbard bands. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Failure of the standard model Mott transition in V 2 O 3 under pressure

Failure of the standard model Mott transition in V 2 O 3 under pressure or chemical substitution on V-site THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Mott transition in layered organic conductors al. cond-mat/0004455, Phys. Rev. Lett. 85, 5420 (2000)

Mott transition in layered organic conductors al. cond-mat/0004455, Phys. Rev. Lett. 85, 5420 (2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS S Lefebvre et

Failure of the Standard and Model: Ni. Se. Miyasaka S 2 -x x (2000)

Failure of the Standard and Model: Ni. Se. Miyasaka S 2 -x x (2000) Takagi THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Failure of the standard model : Anomalous Resistivity: Li. V 2 O 4 Takagi

Failure of the standard model : Anomalous Resistivity: Li. V 2 O 4 Takagi et. al. PRL 2000 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Failure of the Standard Model: Anomalous Spectral Weight Transfer Optical Conductivity o of Fe.

Failure of the Standard Model: Anomalous Spectral Weight Transfer Optical Conductivity o of Fe. Si for T=, 20, 250 200 and 250 K from Schlesinger et. al (1993) Neff depends on T THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Strong Correlation Problem n n Large number of compounds (d, f, p…. ). Qualitative

Strong Correlation Problem n n Large number of compounds (d, f, p…. ). Qualitative and quantitive failures of the standard model. Treat the itinerant and localized aspect of the electron The Mott transition, head on confrontation with this issue Dynamical Mean Field Theory simplest approach interpolating between bands and atoms with open shells. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Hubbard model q. U/t q. Doping d or chemical potential q. Frustration (t’/t) q.

Hubbard model q. U/t q. Doping d or chemical potential q. Frustration (t’/t) q. T temperature Mott transition as a function of doping, pressure RUTGERS temperature etc. THE STATE UNIVERSITY OF NEW JERSEY

Limit of large lattice coordination Metzner Vollhardt, 89 Muller-Hartmann 89 THE STATE UNIVERSITY OF

Limit of large lattice coordination Metzner Vollhardt, 89 Muller-Hartmann 89 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Dynamical Mean Field Theory, cavity construction A. Georges G. Kotliar Phys. Rev. B 45,

Dynamical Mean Field Theory, cavity construction A. Georges G. Kotliar Phys. Rev. B 45, 6497, 1992 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

Phys. Rev. B 45, 6497 A. Georges, G. Kotliar (1992) Mean-Field : Classical vs Quantum case Classical case THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Solving the DMFT equations • Wide variety of computational tools (QMC, NRG, ED…. )Analytical

Solving the DMFT equations • Wide variety of computational tools (QMC, NRG, ED…. )Analytical Methods • Extension to ordered states. Review: A. Georges, G. Kotliar, W. Krauth and M. Rozenberg Rev. Mod. Phys. 68, 13 (1996)] n THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Single site DMFT, functional formulation. Construct a functional of the local Greens function n

Single site DMFT, functional formulation. Construct a functional of the local Greens function n Expressed in terms of Weiss field (semicircular. DOS) [G. Kotliar EBJB 99] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Insights from DMFT q Low temperatures several competing phases. Their relative stability depends on

Insights from DMFT q Low temperatures several competing phases. Their relative stability depends on chemistry and crystal structure q. High temperature behavior around Mott endpoint, more universal regime, captured by simple models treated within DMFT THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Schematic DMFT phase diagram Hubbard model (partial frustration) M. Rozenberg G. Kotliar H. Kajueter

Schematic DMFT phase diagram Hubbard model (partial frustration) M. Rozenberg G. Kotliar H. Kajueter G Tahomas D. Rapkikne J Honig and P Metcalf Phys. Rev. Lett. 75, 105 (1995) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Kuwamoto Honig and Appell PRB (1980) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Kuwamoto Honig and Appell PRB (1980) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Phase Diag: Ni Se 2 -x Sx THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Phase Diag: Ni Se 2 -x Sx THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Insights from DMFT q. The Mott transition is driven by transfer of spectral weight

Insights from DMFT q. The Mott transition is driven by transfer of spectral weight from low to high energy as we approach the localized phase q. Control parameters: doping, temperature, pressure… THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Evolution of the Spectral Function with Temperature Anomalous transfer of spectral weight connected to

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) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous transfer of optical spectral weight, Ni. Se. S. [Miyasaka and Takagi] THE STATE

Anomalous transfer of optical spectral weight, Ni. Se. S. [Miyasaka and Takagi] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous transfer of optical spectral weight V 2 O 3 : M Rozenberg G.

Anomalous transfer of optical spectral weight V 2 O 3 : 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) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

. ARPES measurements on Ni. S 2 -x. Sex Matsuura et. Al Phys. Rev

. ARPES measurements on Ni. S 2 -x. Sex Matsuura et. Al Phys. Rev B 58 (1998) 3690 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Insights from DMFT: think in term of spectral functions (branch cuts) instead of well

Insights from DMFT: think in term of spectral functions (branch cuts) instead of well defined QP (poles ) Resistivity near the metal insulator endpoint ( Rozenberg et. al 1995) exceeds the Mott limit THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous Resistivity and Mott transition Ni Se 2 -x Sx THE STATE UNIVERSITY OF

Anomalous Resistivity and Mott transition Ni Se 2 -x Sx THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous transfer of optical spectral weight V 2 O 3 : M Rozenberg G.

Anomalous transfer of optical spectral weight V 2 O 3 : 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) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Insights from DMFT n n n Mott transition as a bifurcation of an effective

Insights from DMFT n n n 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. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

n n Realistic Calculations of the Electronic Structure of Correlated materials Combinining DMFT with

n n Realistic Calculations of the Electronic Structure of Correlated materials Combinining DMFT with state of the art electronic structure methods to construct a first principles framework to describe complex materials. Beyond LDA+U approach (Anisimov, Andersen and Zaanen) Anisimov Poteryaev Korotin Anhokin and Kotliar J. Phys. Cond. Mat. 35, 7359 (1997) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Combining LDA and DMFT The light, SP (or SPD) electrons are extended, well described

Combining LDA and DMFT The light, SP (or SPD) electrons are extended, well described by LDA n The heavy, D (or F) electrons are localized, treat by DMFT. n LDA already contains an average interaction of the heavy electrons, subtract this out by shifting the heavy level (double counting term) The U matrix can be estimated from first principles or viewed as parameters n THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Spectral Density Functional : effective action construction (Fukuda, Valiev and Fernando , Chitra and

Spectral Density Functional : effective action construction (Fukuda, Valiev and Fernando , Chitra and Kotliar). DFT, consider the exact free energy as a functional of an external potential. Express the free energy as a functional of the density by Legendre transformation. GDFT[r(r)] n Introduce local orbitals, ca. R(r-R)orbitals, and local GF G(R, R)(i w) = n The exact free energy can be expressed as a functional of the local Greens function and of the density by introducing G[r(r), G(R, R)(iw)] n A useful approximation to the exact functional can be constructed, the DMFT +LDA functional. Savrasov Kotliar and n Abrahams Nature 410, 793 (2001)) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

LDA+DMFT Self-Consistency loop E U DMFT THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

LDA+DMFT Self-Consistency loop E U DMFT THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Case study in f electrons, Mott transition in the actinide series. B. Johanssen 1974

Case study in f electrons, Mott transition in the actinide series. B. Johanssen 1974 Smith and Kmetko Phase Diagram 1984. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Total energy vs Volume (Savrasov Kotliar and Abrahams Nature 410, 793 (2001)) THE STATE

Total energy vs Volume (Savrasov Kotliar and Abrahams Nature 410, 793 (2001)) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Small amounts of Ga stabilize the d phase THE STATE UNIVERSITY OF NEW JERSEY

Small amounts of Ga stabilize the d phase THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Problems with density functional treatements of d Pu DFT in the LDA or GGA

Problems with density functional treatements of d Pu DFT in the LDA or GGA is a well established tool for the calculation of ground state properties. • Many studies (APW Freeman, Koelling 1972, ASA and FPLMTO, Soderlind et. al 1990, Kollar et. al 1997, Boettger et. al 1998, Wills et. al. 1999) show • an equilibrium volume of the d phase Is 35% lower than experiment • This is the largest discrepancy ever known in DFT based calculations. • LSDA predicts magnetic long range order which is not observed experimentally (Solovyev et. al. ) • If one treats the f electrons as part of the core LDA overestimates the volume by 30% • Weak correlation picture for alpha phase. •

Pu DMFT total energy vs Volume (Savrasov Kotliar and Abrahams Nature 410, 793 (2001)

Pu DMFT total energy vs Volume (Savrasov Kotliar and Abrahams Nature 410, 793 (2001) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Lda vs Exp Spectra (Joyce et. al. ) THE STATE UNIVERSITY OF NEW JERSEY

Lda vs Exp Spectra (Joyce et. al. ) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Pu Spectra DMFT(Savrasov) EXP (Joyce , Arko et. al) THE STATE UNIVERSITY OF NEW

Pu Spectra DMFT(Savrasov) EXP (Joyce , Arko et. al) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Case study Fe and Ni n n n Archetypical itinerant ferromagnets LSDA predicts correct

Case study Fe and Ni n n n 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 much larger than the ordered moment. Magnetic anisotropy THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Iron and Nickel: crossover to a real space picture at high T (Lichtenstein, Katsnelson

Iron and Nickel: crossover to a real space picture at high T (Lichtenstein, Katsnelson and Kotliar Phys Rev. Lett 87, 67205 , 2001) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Iron and Nickel: magnetic properties (Lichtenstein, Katsenelson, GK PRL 01) THE STATE UNIVERSITY OF

Iron and Nickel: magnetic properties (Lichtenstein, Katsenelson, GK PRL 01) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Ni and Fe: theory vs exp n n n m/ m. B ordered moment

Ni and Fe: theory vs exp n n n m/ m. B ordered moment Fe 2. 5 ( theory) Ni. 6 (theory) meff / m. B 2. 2(expt). 6(expt) high T moment Fe 3. 1 (theory) 3. 12 (expt) Ni 1. 5 (theory) 1. 62 (expt) Curie Temperature Tc n n Fe 1900 Ni 700 ( theory) (theory) 1043(expt) 631 (expt) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Fe and Ni Consistent picture of Fe (more localized) and Ni (more correlated) n

Fe and Ni Consistent picture of Fe (more localized) and Ni (more correlated) n Satellite in minority band at 6 ev, 30 % reduction of bandwidth, exchange splitting reduction. 3 ev n Spin wave stiffness controls the effects of spatial flucuations, it is about twice as large in Ni and in Fe n Mean field calculations using measured exchange constants(Kudrnovski Drachl PRB 2001) right Tc for Ni but overestimates Fe , RPA corrections reduce Tc of Ni by 10% and Tc of Fe by 50%. n THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Photoemission Spectra and Spin Autocorrelation: Fe (U=2, J=. 9 ev, T/Tc=. 8) (Lichtenstein, Katsenelson,

Photoemission Spectra and Spin Autocorrelation: Fe (U=2, J=. 9 ev, T/Tc=. 8) (Lichtenstein, Katsenelson, Kotliar Phys Rev. Lett 87, 67205 , 2001) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Photoemission and T/Tc=. 8 Spin Autocorrelation: Ni (U=3, J=. 9 ev) THE STATE UNIVERSITY

Photoemission and T/Tc=. 8 Spin Autocorrelation: Ni (U=3, J=. 9 ev) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Summary n n n Introduction to strongly correlated electrons Dynamical Mean Field Theory Model

Summary n n n Introduction to strongly correlated electrons Dynamical Mean Field Theory Model Hamiltonian Studies. Universal aspects insights from DMFT System specific studies: LDA+DMFT Outlook THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Outlook q The Strong Correlation Problem: How to deal with a multiplicity of competing

Outlook q The Strong Correlation Problem: How to deal with a multiplicity of competing low temperature phases and infrared trajectories which diverge in the IR q. Strategy: advancing our understanding scale by scale q. Generalized cluster methods to capture longer range magnetic correlations q. New structures in k space. Cellular DMFT THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Challenges n n Short Range Magnetic Correlations without magnetic order. Single Site DMFT does

Challenges n n Short Range Magnetic Correlations without magnetic order. Single Site DMFT does not capture these effects THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Outlook n n n Extensions to take into account longer range correlations and interactions

Outlook n n n Extensions to take into account longer range correlations and interactions [ Cellular DMFT G. Kotliar S. Savrasov G. Palsson and G. Biroli Phys. Rev. Lett. 87, 186401, 2001] Mott transition magnetic correlations and momentum space differentiation. RVB, multipatch models of transport A. Perali M. Sindel and G. Kotliar Eur. Phys. J. B 24, 487 (2001). Exploration of materials. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Acknowledgements Collaborators: V. Anisimov, R. Chitra, V. Dobrosavlevic, D. Fisher, A. Georges, H. Kajueter,

Acknowledgements Collaborators: V. Anisimov, R. Chitra, V. Dobrosavlevic, D. Fisher, A. Georges, H. Kajueter, W. Krauth, E. Lange, G. Moeller, Y. Motome, G. Palsson, M. Rozenberg, S. Savrasov, Q. Si, V. Udovenko, X. Y. Zhang Support: National Science Foundation. Work on Fe and Ni: Office of Naval Research Work on Pu: Departament of Energy and LANL. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

LDA+DMFT functional F Sum of local 2 PI graphs with local U matrix and

LDA+DMFT functional F Sum of local 2 PI graphs with local U matrix and local G THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Comments on LDA+DMFT • • Static limit of the LDA+DMFT functional , with F=

Comments on LDA+DMFT • • Static limit of the LDA+DMFT functional , with F= FHF reduces to LDA+U Removes inconsistencies and shortcomings of this approach. DMFT retain correlations effects in the absence of orbital ordering. • • 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. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous Resistivities: Doped Hubbard Model (QMC) Prushke and Jarrell 1993 THE STATE UNIVERSITY OF

Anomalous Resistivities: Doped Hubbard Model (QMC) Prushke and Jarrell 1993 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

RUTGERS THE STATE UNIVERSITY OF NEW JERSEY other types of printers. cript printer, but

RUTGERS THE STATE UNIVERSITY OF NEW JERSEY other types of printers. cript printer, but not to Comment: was not saved a preview included in it. Preview: Creator: gnuplot Title: IPT NCA Anomalous Resistivities: Doped Hubbard Model G. Palsson 1998

DMFT: Methods of Solution THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

DMFT: Methods of Solution THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

LDA functional Conjugate field, VKS(r) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

LDA functional Conjugate field, VKS(r) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Minimize LDA functional Kohn Sham eigenvalues, auxiliary THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Minimize LDA functional Kohn Sham eigenvalues, auxiliary THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous transfer of spectral weight heavy fermions THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous transfer of spectral weight heavy fermions THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous transfer of spectral weight THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous transfer of spectral weight THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous transfer of spectral weigth heavy fermions THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Anomalous transfer of spectral weigth heavy fermions THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

V 2 O 3 resistivity THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

V 2 O 3 resistivity THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

LDA+DMFT Self-Consistency loop E U DMFT THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

LDA+DMFT Self-Consistency loop E U DMFT THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

DMFT Impurity cavity construction: A. Georges, G. Kotliar, PRB, (1992)] Weiss field THE STATE

DMFT Impurity cavity construction: A. Georges, G. Kotliar, PRB, (1992)] Weiss field THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Spectral Evolution at T=0 half filling full frustration X. Zhang M. Rozenberg G. Kotliar

Spectral Evolution at T=0 half filling full frustration X. Zhang M. Rozenberg G. Kotliar (PRL 1993) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Parallel development: Fujimori et. al THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Parallel development: Fujimori et. al THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Landau Functional G. Kotliar EPJB (1999) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Landau Functional G. Kotliar EPJB (1999) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Ni and Fe: theory vs exp n n n m( T=. 9 Tc)/ m.

Ni and Fe: theory vs exp n n n m( T=. 9 Tc)/ m. B ordered moment Fe 1. 5 ( theory) Ni. 3 (theory) meff / m. B 1. 55 (expt). 35 (expt) high T moment Fe 3. 1 (theory) 3. 12 (expt) Ni 1. 5 (theory) 1. 62 (expt) Curie Temperature Tc n n Fe 1900 Ni 700 ( theory) (theory) 1043(expt) 631 (expt) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Problems with LDA o o o DFT in the LDA or GGA is a

Problems with LDA o o o DFT in the LDA or GGA is a well established tool for the calculation of ground state properties. Many studies (Freeman, Koelling 1972)APW methods ASA and FP-LMTO Soderlind et. Al 1990, Kollar et. al 1997, Boettger et. al 1998, Wills et. al. 1999) give an equilibrium volume of the d phase Is 35% lower than experiment This is the largest discrepancy ever known in DFT based calculations. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

Spectral Density Functional n n n The exact functional can be built in perturbation

Spectral Density Functional n n n The exact functional can be built in perturbation theory in the interaction (well defined diagrammatic rules )The functional can also be constructed expanding around the atomic limit. No explicit expression exists. DFT is useful because good approximations to the exact density functional GDFT[r(r)] exist, e. g. LDA, GGA A useful approximation to the exact functional can be constructed, the DMFT +LDA functional. Savrasov Kotliar and Abrahams Nature 410, 793 (2001)) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

LDA functional Conjugate field, VKS(r) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

LDA functional Conjugate field, VKS(r) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS