-
What is DMFT ?
-
Dynamical Mean Field Theory (DMFT) is a fruitful non perturbative approach to strongly
correlated electrons systems. It is a local approximation in space which reduces a microscopic model
on a lattice to a self-consistent quantum impurity model. It describes both the localised and the itinerant limit
of electronic problems. It has already produced remarkable results and predictions on the Mott transition problem.
- Why going beyond DMFT ?
-
However, in spite of these successes, various limitations of single site DMFT are now apparent.
For example, the self-energy is independant of the momentum k by construction. Therefore, the method
can not describe independant variations of quasi-particle residue and effective mass in the Fermi liquid regime.
Moreover, a single site effective model preclude the treatment of more exotic orders with a order parameters
which extends on a few sites, like dimerization, staggered flux, d-density wave or d-wave superconductivity which is
observed experimentally in high-Tc superconductors.
- Cluster methods
-
To overcome these limitations, we study cluster extensions of DMFT (CDMFT), using a self-consistent cluster of sites.
These extensions will allow a more refined treatment of the Mott transition, in particular in its aspects depending on k,
and of instabilities towards others phases (like superconductivity) and their relation with the Mott transition
- Theoretical methods
-
The main technical difficulty is to find a efficient and reliable method to solve the self-consistent
impurity problem. Even though quantum impurity models have been long studied, many useful methods are useless for DMFT
problems, including integrability and Conformal Field Theory, because of the self-consistent aspect of the problem.
New techniques are now being developped.
- Main collaborators
-
References
- A. Georges, G. Kotliar, W. Krauth and M. J. Rozenberg
Rev. Mod. Phys. 68 13 (1996).
|
