In- and out-of-equilibrium ab initio theory of electrons and phonons

We lay down the ab initio many-body quantum theory of electrons and phonons in equilibrium as well as in steady-state or time-varying settings [1]. The focus is on the harmonic approximation, but the developed tools can readily incorporate anharmonic effects. We begin by showing the necessity of determining the ab initio Hamiltonian in a self-consistent manner to ensure the existence of an equilibrium state. We then identify the correct partitioning into a “noninteracting” and an “interacting” part to carry out diagrammatic expansions in terms of dressed propagators and screened interactions. The final outcome is the finite-temperature nonequilibrium extension of the Hedin equations, showcasing the emergence of the coupling between electrons and coherent phonons through the time-local Ehrenfest diagram. We also derive the Kadanoff-Baym equations, discuss the theory of conserving approximations, and highlight the simplifications leading to the Born-Oppenheimer approximation as well as the semiconductor Bloch and Boltzmann equations.

[1] G. Stefanucci, R. van Leeuwen and E. Perfetto, Phys. Rev. X 13, 031026 (2023)