Strongly Correlated Electron Systems a Dynamical Mean Field Perspective:Points for Discussion

1. Strongly Correlated Electron Systems a Dynamical Mean Field Perspective:Points for Discussion G. Kotliar Physics Department and Center for Materials Theory Rutgers ICAM meeting: Frontiers in Correlated Matter Snowmass September 2004

2. Strongly Correlated Electron Systems Display remarkable phenomena, that cannot be understood within the standard model of solids. Resistivities that rise without sign of saturation beyond the Mott limit, (e.g. H. Takagi’s work on Vanadates), temperature dependence of the integrated optical weight up to high frequency (e.g. Vandermarel’s work on Silicides). Correlated electrons do “big things”, large volume collapses, colossal magnetoresitance, high temperature superconductivity . Properties are very sensitive to structure chemistry and stoichiometry, and control parameters large non linear susceptibilites

3. Strongly correlated materials display remarkable phenomena,not describable by the standard model. How to think about their electronic states ? How to compute their properties ? Mapping onto connecting their properties, a simpler “reference system”. A self consistent impurity model living on SITES, LINKS and PLAQUETTES...... DYNAMICAL MEAN FIELD THEORY. "Optimal Gaussian Medium " + " Local Quantum Degrees of Freedom " + "their interaction " is a good reference frame for understanding, and predicting physical properties of correlated materials. Focus on local quantities, construct functionals of those quantities, similarities with DFT.

4. Points for discussion arising from this perspective • Single site DMFT. High temperature universality vs low temperature sensitivity to realistic modelling, of materials near a temperature-pressure driven Mott transition.[V2O3, NiSeS, k-organics]. Top to bottom view of the strong correlation problem. • C-DMFT a rapidly convergent algorithm for solving the many body problem ? Will we be able to at least identify trends, in the physical properties of correlated materials starting from first principles ? How about trends in quantities such as critical temperatures ? Will we be have nearly the same success as density functional based methods for weakly correlated systems. • Plaquette DMFT. Momentum space differentiation, i.e. generation of strong anisotropy on the fermi surface, is an unavoidable consequence of the proximity to the Mott transition .[Kappa organics and cuprates]. Will we be able to achieve good momentum space resolution with real space methods ?

5. Mott transition across the 5f’s, a very interesting playground for studying correlated electron phenomena. • DMFT ideas have been extended into a framework capable of making first principles first principles studies of correlated materials. Pu Phonons. Combining theory and experiments to separate the contributions of different energy scales, and length scales to the bonding • In single site DMFT , superconductivity is an unavoidable consequence when we try to go move from a metallic state to a Mott insulator where the atoms have a closed shell (no entropy). Realization in Am under pressure ?

6. Making connections with phenomenological models of materials, doped semiconductors (Bhatt and Sachdev), heavy fermions (Nakatsuji, Pines and Fisk )……