Download Correlated Electrons: A Dynamical Mean Field (DMFT) Perspective

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
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
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.
Points for
discussion
arising fromuniversality
this perspectivevs low
• Single site DMFT.
High
temperature
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 ?
• 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 ?
• Making connections with
phenomenological models of materials,
doped semiconductors (Bhatt and
Sachdev), heavy fermions (Nakatsuji,
Pines and Fisk )……