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arXiv · 1803.07364

Coupled Kohn-Sham equations for electrons and phonons

Chung-Yu Wang·T. Müller·Sangeeta Sharma·E. K. U. Gross·J. K. Dewhurst
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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.

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Chung-Yu Wang, T. Müller, Sangeeta Sharma, E. K. U. Gross, J. K. Dewhurst. 2018-03-20. Coupled Kohn-Sham equations for electrons and phonons. https://arxiv.org/abs/1803.07364

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