Transcript Document

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 theory
Implementation
∑(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:
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.
Transport Quantities
• Linear response – Kubo formula
Find the current-current correlation function.
• Optical Conductivity
• DC Conductivity = ω 0 limit of Optical
Conductivity.
Numerical implementation