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

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Strongly Correlated Electron Systems a
Dynamical Mean Field PerspectivePoints for
Discussion

• G. Kotliar
• Physics Department and Center for Materials
  Theory
• Rutgers

ICAM meeting Frontiers in Correlated Matter
Snowmass September 2004
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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.
Takagis work on Vanadates), temperature
dependence of the integrated optical weight up
to high frequency (e.g. Vandermarels 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
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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.

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• 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
  ?

Points for discussion arising from this
perspective
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• Mott transition across the 5fs, 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 ?

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