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

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

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

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

5. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Single site DMFT, functional formulation Express in terms of Weiss field (semicircularDOS) The Mott transition as bifurcation point in functionals o  G  or F[  ], (G. Kotliar EPJB 99) Local self energy (Muller Hartman 89)

6. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Review of DMFT, technical tools for solving DMFT eqs.., applications, references…… A. Georges, G. Kotliar, W. Krauth and M. Rozenberg Rev. Mod. Phys. 68,13 (1996)]

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

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

9. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Schematic DMFT phase diagram Hubbard model (partial frustration) Rozenberg et.al. PRL (1995)

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

11. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Phase Diag: Ni Se 2-x S x

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

13. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS 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 2000)

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

15. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS 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

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

17. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Insights from DMFT 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. –

18. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS DMFT  Spin Orbital Ordered States  Longer range interactions Coulomb, interactions, Random Exchange (Sachdev and Ye, Parcollet and Georges, Kajueter and Kotliar, Si and Smith, Chitra and Kotliar,)  Short range magnetic correlations. Cluster Schemes. (Ingersent and Schiller, Georges and Kotliar, cluster expansion in real space, momentum space cluster DCA Jarrell et.al., C-DMFT Kotliar et. al ).

19. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS DMFT  Formulation as an electronic structure method (Chitra and Kotliar)  Density vs Local Spectral Function  Extensions to treat strong spatial inhomogeneities. Anderson Localization (Dobrosavlevic and Kotliar),Surfaces (Nolting),Stripes (Fleck Lichtenstein and Oles)  Practical Implementation (Anisimov and Kotliar, Savrasov, Katsenelson and Lichtenstein)

20. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Anomalous Resistivity:LiV 2 O 4 Takagi et.al. PRL 2000

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

22. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Anomalous Resistivities: Doped Hubbard Model G. Palsson 1998 IPT NCA

23. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Failure of the “Standard Model”: Cuprates Anomalous Resistivity

24. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Specific Heat Titanates

25. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Mott transition in layered organic conductors S Lefebvre et al. cond-mat/0004455

26. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

27. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Standard Model Typical Mott values of the resistivity 200  Ohm- cm Residual instabilites SDW, CDW, SC Odd # electrons -> metal Even # electrons -> insulator  Theoretical foundation: Sommerfeld, Bloch and Landau  Computational tools DFT in LDA  Transport Properties, Boltzman equation, low temperature dependence of transport coefficients

28. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Failure of the “Standard Model”: Cuprates Anomalous Resistivity

29. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Solving the DMFT equations Wide variety of computational tools (QMC, NRG,ED….) Analytical Methods

30. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS DMFT  Formulation as an electronic structure method (Chitra and Kotliar)  Density vs Local Spectral Function  Extensions to treat strong spatial inhomogeneities. Anderson Localization (Dobrosavlevic and Kotliar),Surfaces (Nolting),Stripes (Fleck Lichtenstein and Oles)  Practical Implementation (Anisimov and Kotliar, Savrasov, Katsenelson and Lichtenstein)

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

32. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS DMFT  Spin Orbital Ordered States  Longer range interactions Coulomb, interactions, Random Exchange (Sachdev and Ye, Parcollet and Georges, Kajueter and Kotliar, Si and Smith, Chitra and Kotliar,)  Short range magnetic correlations. Cluster Schemes. (Ingersent and Schiller, Georges and Kotliar, cluster expansion in real space, momentum space cluster DCA Jarrell et.al., C-DMFT Kotliar et. al ).

33. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Strongly Correlated Electrons  Competing Interaction  Low T, Several Phases Close in Energy  Complex Phase Diagrams  Extreme Sensitivity to Changes in External Parameters  Need for Quantitative Methods

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

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

36. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS LDA functional Conjugate field, V KS (r)

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

38. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS A time-honored example: Mott transition in V 2 O 3 under pressure or chemical substitution on V-site

39. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Ising character of the transfer of spectral weight Ising –like dependence of the photo-emission intensity and the optical spectral weight near the Mott transition endpoint

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

41. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Photoemission LaTiO3

42. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS