Coupled Kohn-Sham equations for electrons and phonons
Abstract
This work establishes the algebraic structure of the Kohn-Sham equations to be solved in a density formulation of electron and phonon dynamics, including the superconducting order parameter. A Bogoliubov transform is required to diagonalize both the fermionic and bosonic Kohn-Sham Hamiltonians since they both represent a non-interacting quantum field theory. The Bogoliubov transform for phonons is non-Hermitian in the general case, and the corresponding time-evolution is non-unitary. Several sufficient conditions for ensuring that the bosonic eigenvalues are real are provided and a practical method for solving the system is described. Finally, we produce a set of approximate mean-field potentials which are functionals of the electronic and phononic density matrices and depend on the electron-phonon vertex.
Cite
@article{arxiv.1803.07364,
title = {Coupled Kohn-Sham equations for electrons and phonons},
author = {Chung-Yu Wang and T. Müller and Sangeeta Sharma and E. K. U. Gross and J. K. Dewhurst},
journal= {arXiv preprint arXiv:1803.07364},
year = {2018}
}