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Extended Dynamical Mean Field

Extended Dynamical Mean Field. Metal-insulator transition. el-el correlations not important : band insulator: the lowest conduction band is full gap due to the periodic potential – few eV even number electrons metal Conduction band partially occupied. zt.

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Extended Dynamical Mean Field

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  1. Extended Dynamical Mean Field

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

  3. Doping Mott insulator – DMFT perspective • Metallic system always Fermi liquid ImS(w)w2 • Fermi surface unchanged (volume and shape) • Narrow quasiparticle peak of width ZeFd at the Fermi level • Effective mass (m*/m1/Z) diverges at the transition • High-temperature (T>> ZeF) almost free spin LHB UHB quasip. peak d Georges, Kotliar, Krauth and Rozenberg 1996

  4. mean-field description of the exchange term is exact within DMFT 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  2N deg. states) Why? Metzner Vollhardt 89 J disappears completely in the paramagnetic phase!

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

  6. mapping fermionic bath bosonic bath fluctuating magnetic field Extended DMFT J and t equally important: 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 A(k,0) A(k,) ky k kx

  13. A(k,) =0.04 A(k,0) A(k,) ky k kx

  14. A(k,) =0.06 A(k,0) A(k,) ky k kx

  15. A(k,) =0.08 A(k,0) A(k,) ky k kx

  16. A(k,) =0.10 A(k,0) A(k,) ky k kx

  17. A(k,) =0.12 A(k,0) A(k,) ky k kx

  18. A(k,) =0.14 A(k,0) A(k,) ky k kx

  19. A(k,) =0.16 A(k,0) A(k,) ky k kx

  20. A(k,) =0.18 A(k,0) A(k,) ky k kx

  21. A(k,) =0.20 A(k,0) A(k,) ky k kx

  22. A(k,) =0.22 A(k,0) A(k,) ky k kx

  23. A(k,) =0.24 A(k,0) A(k,) ky k kx

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

  25.  &  EMDT+NCA ED 20 sites

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

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