Introduction to TDDFT Linear-Response TDDFT in Frequency-Reciprocal space on a Plane-Waves basis: the DP (Dielectric Properties) code Valerio Olevano CNRS, Institut Néel, Grenoble, France 2 Résumé ● Motivation ● TDDFT ● Linear-Response TDDFT ● Frequency-Reciprocal space TDDFT ● TDDFT on a Plane Waves basis: the DP code ● Approximations: RPA, ALDA, new kernels ● Results ● Conclusions
[email protected] Condensed Matter: 3 a Formidable Many-Body Problem ● Well known interaction: electromagnetic (like in QED) ● All our ignorance in Cond-Mat has roots into the many-body problem.
[email protected] 4 the Many-Body Problem ● Already a problem in Classical Physics: 3-body problem (Euler, Lagrange, …) and on ● In Quantum Mechanics even 2 bodies is a problem
[email protected] The Many-Body problem 5 kinetic e-ions many-body interaction e-e interaction where N can be up to the Avogadro number 1023!!! many-body wavefunction
[email protected] 6 The Many-Body problem Factorizable Hamiltonian Solvable single-particle Schrödinger equation Many-body ground-state total energy Total many-body ground state wavefunction Condensed Matter 7 Theory Models Ab Initio (first principles) simplify and search (if possible) numerical solution but analytical solutions microscopic Hamiltonian ● Quantum Chemistry: ● Anderson CI ● Hubbard CC DMFT Subject Headings: … ● Kondo ● QMC ● Ising ● Density-Functional: ● Heisenberg DFT TDDFT ● Many-body Green function: adjustable GW parameters BSE approximations (U, J, ...) (LDA, ...) 8 Why do we need ab initio theories? 1) To understand and explain observed phenomena; 2) To offer experimentalists reference data; 3) To predict properties before the synthesis, the experiment.