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Concept
Dynamical mean-field theory
Summary
Dynamical mean-field theory (DMFT) is a method to determine the electronic structure of strongly correlated materials. In such materials, the approximation of independent electrons, which is used in density functional theory and usual band structure calculations, breaks down. Dynamical mean-field theory, a non-perturbative treatment of local interactions between electrons, bridges the gap between the nearly free electron gas limit and the atomic limit of condensed-matter physics.
DMFT consists in mapping a many-body lattice problem to a many-body local problem, called an impurity model. While the lattice problem is in general intractable, the impurity model is usually solvable through various schemes. The mapping in itself does not constitute an approximation. The only approximation made in ordinary DMFT schemes is to assume the lattice self-energy to be a momentum-independent (local) quantity. This approximation becomes exact in the limit of lattices with an infinite coordination.
One of DMFT's main successes is to describe the phase transition between a metal and a Mott insulator when the strength of electronic correlations is increased. It has been successfully applied to real materials, in combination with the local density approximation of density functional theory.
The DMFT treatment of lattice quantum models is similar to the mean-field theory (MFT) treatment of classical models such as the Ising model. In the Ising model, the lattice problem is mapped onto an effective single site problem, whose magnetization is to reproduce the lattice magnetization through an effective "mean-field". This condition is called the self-consistency condition. It stipulates that the single-site observables should reproduce the lattice "local" observables by means of an effective field. While the N-site Ising Hamiltonian is hard to solve analytically (to date, analytical solutions exist only for the 1D and 2D case), the single-site problem is easily solved.
Likewise, DMFT maps a lattice problem (e.g. the Hubbard model) onto a single-site problem.
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