Challenges%20in%20Strongly%20Correlated%20Electron%20Systems:%20A%20Dynamical%20Mean%20Field%20Theory%20Perspective

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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

EPS 21st General Conference of the Condensed
matter Division and DPG Spring Meeting March 26
- 31, 2006 In Dresden, Germany
upport NSF -DMR DOE-Basic Energy Sciences .
Chaire Blaise Pascal Fondation de lEcole
Normale.
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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 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 how does the electron go from
the localized to itinerant ?
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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 d8 Metzner and
Vollhardt (1989)
Reviews A. Georges W. Krauth G.Kotliar and M.
Rozenberg RMP (1996)G. Kotliar and D. Vollhardt
Physics Today (2004).
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Mean-Field Classical vs Quantum
Classical case
Quantum case
Hard!!!
Easy!!!
QMC J. Hirsch R. Fye (1986) NCA T. Pruschke
and N. Grewe (1989) PT Yoshida and Yamada
(1970) NRG Wilson (1980)
A. Georges, G. Kotliar (1992)
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DMFT Qualitative Phase diagram of a frustrated
Hubbard model at integer filling

T/W
Synthesis Brinkman Rice Hubbard Castellani
et.al. Kotliar Ruckenstein Fujimori
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Interaction with Experiments. V2O3Anomalous
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)
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Photoemission measurements and Theory
V2O3 Mo, Denlinger, Kim, Park, Allen, Sekiyama,
Yamasaki, Kadono, Suga, Saitoh, Muro, Metcalf,
Keller, Held, Eyert, Anisimov, Vollhardt PRL .
(2003)
.
NiSxSe1-xMatsuura Watanabe Kim Doniach Shen Thio
Bennett (1998)
Poteryaev et.al. (to be published)
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Spinodals and Ising critical endpoint. Theory
Castellani et.al PRL 43, 1957 (1979)
Kotliar et.al. PRL84, 5180 (2003)
Observation in V2O3 P. Limelette et.al.
Science 302, 89 (2003)
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Electronic Structure Meets DMFT

• LDADMFT

• Functional formulations, life without U

• Further extensions, clusters, GWDMFT

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.
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Localization Delocalization in the Actinides
The f electrons in Plutonium are close to a
localization-delocalization transition
(Johansson, 1974) .
Mott Transition
d
a
after G. Lander, Science (2003).
Modern understanding of this phenomena using
functional approach toDMFT. Savrasov et.al.
(2001-2005)
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DMFT Phonons in fcc d-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)
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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 Georges et.al. RMP(1996). Th. Maier, M.
Jarrell, Th.Pruschke, M.H. Hettler RMP (2005)
Kotliar Savrasov et. .al. RMP in Press.
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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)
U/t4.
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Doping Driven Mott transiton at low temperature,
in 2d (U16 t1, t-.3 ) Hubbard model
Spectral Function A(k,??0) -1/p G(k, ? ?0) vs k
K.M. Shen et.al. 2004
Antinodal Region
2X2 CDMFT
Nodal Region
Civelli et.al. PRL 95 (2005)
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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 ?