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

by Gianluca Stefanucci (ROMA2)




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. 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. The Hedin equations have limited practical utility for real-time simulations 
of systems driven out of equilibrium by external fields. We then derive the Kadanoff-Baym equations 
for electrons and phonons, discuss the theory of conserving approximations and show how to 
recover the Born-Oppenheimer approximation. We conclude by pointing out a possible 
correlation-induced splitting of the phonon dispersion in materials with no time-reversal