IV) Materials calculations with dynamical mean field theory (DMFT)
IV) Materials calculations with dynamical mean field theory (DMFT)
IV) Materials calculations with dynamical mean field theory (DMFT)
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Ab-initio electronic Hamiltonian(non-relativistic/Born-Oppenheimer approximation)kinetic energy lattice potential Coulomb interactionH = X i"− 2 ∆ i2m e+ X l−e 24πɛ 0Z l|r i − R l |#+ 1 2Xi≠je 24πɛ 01|r i − r j |LDA bandstructure corresponds toH LDA = X i"− 2 ∆ i2m e+ X l−e 24πɛ 01|r i − R l | + Zd 3 r#e2 1LDAρ(r) + Vxc (ρ(r i ))4πɛ 0 |r i − r|LDA + local Coulomb interactionĤ = X klmσɛ LDAklm ĉ†klσĉkmσ+ 1 2| {z }H LDAXU σσ′lmi lσmσ ′ˆn ilσ ˆn imσ ′ − ∆ɛ X imσˆn imσU’Um=2U’−Jm=1