Dynamical mean field theory: In practice

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 theoryImplementation ∑(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.

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