1. Extended Dynamical Mean Field

2. Metal-insulator transition el-el correlations not important:  band insulator: the lowest conduction band is fullthe lowest conduction band is full gap due to the periodic potential – few eVgap due to the periodic potential – few eV even number electronseven number electrons  metal Conduction band partially occupiedConduction band partially occupied el-el correlations important:  Mott insulator despite the odd number of electrons  Cannot be explained within a single- electron picture (many body effect) zt F*F*F*F* Zhang, Rozenberg and Kotliar 1992 U

3. Doping Mott insulator – DMFT perspective  Metallic system always Fermi liquid  Im    Fermi surface unchanged (volume and shape)  Narrow quasiparticle peak of width Z  F   at the Fermi level  Effective mass (m*/m  1/Z) diverges at the transition  High-temperature (T>> Z  F ) almost free spin Georges, Kotliar, Krauth and Rozenberg 1996 LHB UHB quasip. peak 

4. Nonlocal interaction in DMFT?  Local quantum fluctuations (between states ) completely taken into account within DMFT  Nonlocal quantum fluctuations (like RKKY) are mostly lost in DMFT (entropy of U=  param. Mott insulator is ln2 and is T independent  2 N deg. states) (entropy of U=  param. Mott insulator is ln2 and is T independent  2 N deg. states) Why? Metzner Vollhardt 89 mean-field description of the exchange term is exact within DMFT J disappears completely in the paramagnetic phase !

5. What is changed by including intersite exchange J? For simplicity we will take infinite U limit and get t-J model: Hubbard model + intersite exchange

6. Extended DMFT J and t equally important: fermionic bath mapping bosonic bath fluctuating magnetic field Q.Si & J.L.Smith 96, H.Kajuter & G.Kotliar 96

7. Still local theory Local quantities can be calculated from the corresponding impurity problem

8. Diagrammatic auxiliary particle impurity solver NCA impurity solver This bubble is zero in the paramagnetic state

9. Pseudogap

10. Local spectral function

11. Luttinger’s theorem?

12. A(k,  )  =0.02 kxkx kyky k A(k,0) A(k,  )

13. A(k,  )  =0.04 kxkx kyky k A(k,0) A(k,  )

14. A(k,  )  =0.06 kxkx kyky k A(k,0) A(k,  )

15. A(k,  )  =0.08 kxkx kyky k A(k,0) A(k,  )

16. A(k,  )  =0.10 kxkx kyky k A(k,0) A(k,  )

17. A(k,  )  =0.12 kxkx kyky k A(k,0) A(k,  )

18. A(k,  )  =0.14 kxkx kyky k A(k,0) A(k,  )

19. A(k,  )  =0.16 kxkx kyky k A(k,0) A(k,  )

20. A(k,  )  =0.18 kxkx kyky k A(k,0) A(k,  )

21. A(k,  )  =0.20 kxkx kyky k A(k,0) A(k,  )

22. A(k,  )  =0.22 kxkx kyky k A(k,0) A(k,  )

23. A(k,  )  =0.24 kxkx kyky k A(k,0) A(k,  )

24. Entropy EMDT+NCA ED 20 sites Experiment: LSCO (T/t*  0.035) J.R. Cooper & J.W. Loram

25.  &  EMDT+NCA ED 20 sites

26. Hall coefficient T~1000K LSCO: T. Nishikawa, J. Takeda & M. Sato (1994)