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Challenges in Strongly Correlated Electron Systems: A Dynamical Mean Field Theory Perspective Challenges in Strongly Correlated Electron Systems: A Dynamical.

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1 Challenges in Strongly Correlated Electron Systems: A Dynamical Mean Field Theory Perspective Challenges in Strongly Correlated Electron Systems: A Dynamical Mean Field Theory Perspective Gabriel Kotliar and Center for Materials Theory & CPHT Ecole Polytechnique Palaiseau & SPHT CEA Saclay, France $upport : NSF -DMR DOE-Basic Energy Sciences. Chaire Blaise Pascal Fondation de l’Ecole Normale. EPS 21st General Conference of the Condensed matter Division and DPG Spring Meeting March 26 - 31, 2006 In Dresden, Germany

2 Fermi Liquid Theory (Landau 1957) Density Functional Theory (Kohn Sham 1964) + [ - ] Static Mean Field Theory. Starting point for perturbation theory in the screened interactions (Hedin 1965) Strong Correlation Challenges Strong Correlation Challenges Approach fails for strongly correlated systems Fermi Liquid Parameters Non Perturbative. Regimes where FLT Does NOT Apply. Need new concepts to replace rigid KS bands !

3 Mott transition: Mott transition: how does the electron go from the localized to itinerant ? Matsuura et. al.(2000) L  -(BEDT-TTF) 2 Cu[N(CN) 2 ]Cl Lefevre et.al. (2000)Limelette et al.,(2003) Kagawa et al. (2003)

4 Dynamical Mean Field Theory. Cavity Construction. A. Georges and G. Kotliar PRB 45, 6479 (1992). Inspiration: Weiss (1907), Onsager (1936), DMFT for spin glasses, Fermions in d=∞ Metzner and Vollhardt (1989) Reviews: A. Georges W. Krauth G.Kotliar and M. Rozenberg RMP (1996)G. Kotliar and D. Vollhardt Physics Today (2004).

5 Classical case Quantum case A. Georges, G. Kotliar (1992) Mean-Field : Classical vs Quantum Easy!!! Hard!!! QMC: J. Hirsch R. Fye (1986) NCA : T. Pruschke and N. Grewe (1989) PT : Yoshida and Yamada (1970) NRG: Wilson (1980) Pruschke et. al Adv. Phys. (1995) Georges et. al RMP (1996) IPT: Georges Kotliar (1992).. QMC: M. Jarrell, (1992), NCA T.Pruschke D. Cox and M. Jarrell (1993), ED:Caffarel Krauth and Rozenberg (1994) Projective method: G Moeller (1995). NRG: R. Bulla et. al. PRL 83, 136 (1999),……………………………………...

6 DMFT Qualitative Phase diagram of a frustrated Hubbard model at integer filling T/W Synthesis: Synthesis: Brinkman Rice Hubbard Castellani et.al. Kotliar Ruckenstein Fujimori

7 Interaction with Experiments. V2O3:Anomalous transfer of spectral weight M. Rozenberg G. Kotliar H. Kajueter G Thomas D. Rapkine J Honig and P Metcalf Phys. Rev. Lett. 75, 105 (1995) T=170 T=300

8 . Photoemission measurements 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 published)

9 Spinodals and Ising critical endpoint. Theory: Castellani et.al PRL 43, 1957 (1979); Kotliar et.al. PRL84, 5180 (2003) Observation in V 2 O 3 : P. Limelette et.al. Science 302, 89 (2003) Spinodals and Ising critical endpoint. Theory: Castellani et.al PRL 43, 1957 (1979); Kotliar et.al. PRL84, 5180 (2003) Observation in V 2 O 3 : P. Limelette et.al. Science 302, 89 (2003)

10 Further extensions, clusters, GW+DMFT … Electronic Structure Meets DMFT LDA+DMFT V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). Lichtentsein and Katsnelson. PRB 57,6884 (1998). Almbladh et.al.(1999), Chitra and Kotliar (2000) (2001). Savrasov Kotliar and Abrahams (2001) Large Number of Groups and Many Compounds have been studied. Functional formulations, life without U

11 Localization Delocalization in the Actinides after G. Lander, Science (2003). The f electrons in Plutonium are close to a localization-delocalization transition (Johansson, 1974). Mott Transition   Modern understanding of this phenomena using functional approach toDMFT. Savrasov et.al. (2001-2005)

12 DMFT Phonons in fcc  -Pu ( Dai, Savrasov, Kotliar,Ledbetter, Migliori, Abrahams, Science, 9 May 2003) Experiments at the European Synchrotron Radiation Facility, (Wong, Krisch, Farber, Occelli, Schwartz,Chiang,Wall, Boro and Xu et.al, Science, 22 August 2003)

13 Cluster DMFTlimitations of single site DMFT Cluster DMFT: removes limitations of single site DMFT No k dependence of the self energy. No d-wave superconductivity. No Peierls dimerization. No (R)valence bonds. Reviews: Reviews: Georges et.al. RMP(1996). Th. Maier, M. Jarrell, Th.Pruschke, M.H. Hettler RMP (2005); Kotliar Savrasov et..al. RMP in Press.

14 U/t=4. Two Site Cellular DMFTin the 1D Hubbard model Two Site Cellular DMFT ( G.. Kotliar et.al. PRL (2001)) in the 1D Hubbard model M.Capone M.Civelli V. Kancharla C.Castellani and GK PRB 69,195105 (2004)

15 Doping Driven Mott transiton at low temperature, in 2d (U=16 t=1, t’=-.3 ) Hubbard model Spectral Function A(k,ω→0)= -1/π G(k, ω →0) vs k K.M. Shen et.al. 2004 2X2 CDMFT Nodal Region Antinodal Region Civelli et.al. PRL 95 (2005)

16 Conclusion Controlled, first principles, many body studies of correlated materials. Finite T Mott transition in 3d. Single site DMFT worked well! Lower T, 2d ? Will CDMFT on a plaquette help us generate the right concepts? New RG methods built around DMFT ?

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