1. Dynamical mean field theory: In practice
N.S.Vidhyadhiraja
Theoretical sciences unit,
JNCASR, Bangalore.

2. Outline Brief review of DMFT Impurity solvers
Iterated perturbation theory
Self energy calculation
Symmetric case
Asymmetric case
Output – Green’s functions, DOS, Transport and thermodynamics
Numerical implementation

3. Dynamical mean field theory Implementation
∑(z)

4. Impurity solvers Iterated perturbation theory (IPT)
Local moment approach
Non-crossing approximation
Exact diagonalization
Quantum Monte Carlo
Numerical Renormalization group
Density-Matrix Renormalization group.

5. Iterated perturbation Theory (IPT)
Iterated perturbation theory at half-filling: Self-energy is just the second order correction built out of Hartree propagators.

9. Equations (1.5), (1.6) and (1.7) do not assume p-h symmetry so they can be used for the asymmetric case as well.

17. References for IPT:

18. Physical observables Green’s functions G(ω)
Spectral function A(ω)= -Im(G(ω))/π
Electronic density of states
Re(G-1(ω))=0 gives Quasiparticle energies.
Z=[{1 - ∂(Re(∑))/∂ω)}ω 0]-1 is the quasiparticle weight and Z-1 is the mass renormalization.

19. Transport Quantities Linear response – Kubo formula
Find the current-current correlation function.
Optical Conductivity
DC Conductivity = ω 0 limit of Optical Conductivity.

20. Numerical implementation