Dynamical mean field theory: In practice

N.S.Vidhyadhiraja

Theoretical sciences unit,

JNCASR, Bangalore.

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

Dynamical mean field theoryImplementation

∑(z)

Impurity solvers

• Iterated perturbation theory (IPT)

• Local moment approach

• Non-crossing approximation

• Exact diagonalization

• Quantum Monte Carlo

• Numerical Renormalization group

• Density-Matrix Renormalization group.

Iterated perturbation Theory (IPT)

• Iterated perturbation theory at half-filling: Self-energy is just the second order correction built out of Hartree propagators.

References for IPT:

• 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.

Physical observables

Transport Quantities

• Linear response – Kubo formula

Find the current-current correlation function.

• Optical Conductivity

• DC Conductivity = ω 0 limit of Optical Conductivity.

Numerical implementation