Exact factorization of a many-body wavefunction beyond the electron-nuclear problem

TL;DR

This paper reviews the exact factorization framework used to analyze complex quantum many-body systems, extending beyond traditional electron-nuclear problems to include electron-only and photon-electron-nuclear systems, highlighting its historical development and recent applications.

Contribution

It provides a comprehensive review of the exact factorization formalism applied to various quantum many-body problems beyond electron-nuclear systems, including recent extensions to photon-electron-nuclear interactions.

Findings

Extended the formalism to electron-only systems.

Applied the framework to molecules in cavity quantum electrodynamics.

Reviewed the historical development and recent applications.

Abstract

This Review is devoted to the presentation of the exact factorization as a framework employed to study a variety of quantum-mechanical many-body problems. Since its original formulation in the 70s, the main applications of the exact factorization were directed towards understanding the properties of multi-component systems, e.g. electron-nuclear systems. Especially in the electron-nuclear case, the exact factorization is viewed as an exactification of the Born-Oppenheimer approximation, thus it was, and still is, largely employed in nonadiabatic dynamics. Nonetheless, as early as the 80s, the formalism was employed to study many-electron interacting systems and, quite recently, i.e. less than a decade ago, it was extended to study the behavior of molecules in the context in cavity quantum electrodynamics. These formulations, perhaps less popular than the electron-nuclear formulation, have attracted a lot of attention over the years. Therefore, we review here the exact electron-only factorization and the exact photon-electron-nuclear factorization.