One of the greatest challenges of condensed-matter physics is to predict the properties of large and complex quantum systems. In modern high-tech societies, essentially all sectors depend on materials with highly specific properties: For example, manmade materials harder than diamond are used in special-purpose drills, highly specific magnetic materials are necessary to make the read/write process in magnetic storage devices as fast as possible. For many purposes, especially in the IT sector, a thorough understanding on the level of the smallest constituents, the electrons and the nuclei, is indispensable. If one aims at a genuine first-principles description based on the fundamental equation of quantum mechanics, the Schrödinger equation, this goal is yet largely unattainable with present-day computing facilities. A variety of highly sophisticated methods such as quantum Monte Carlo, configuration interaction, coupled cluster, tensor networks, Feynman diagrams, dynamical mean-field theory have been developed to deal with the enormous complexity of the quantum many-body problem. For time-dependent scenarios, explicitly time-dependent variants of these methods are available as well. However, due to unfavorable scaling with the number of particles, all of these methods are applicable to small or medium-size systems only. The idea of this action is to attack the many-particle wave function with a novel theoretical approach, known as the exact factorization. In this approach one writes the wavefunction of the full quantum system as a single product of subsystem wavefunctions in such a way that the product is an exact representation of the complete wave function. No approximation is made in this first step. In the case of two subsystems, taking electrons and nuclei as prototypical example, the nuclear factor is a regular wavefunction, satisfying a standard time-dependent Schrödinger equation, while the electronic factor is a conditional probability amplitude that satisfies a more complicated Schrödinger-like equation with a non-linear and non-Hermitian Hamiltonian. The above-mentioned standard techniques can then be applied to the subsystem-Schrödinger equations, typically different standard techniques to different subsystems. The objective of this action is to exploit the exact factorization in various, particularly challenging situations such as solids with strong long-range correlations as well as molecular processes with strong non-adiabatic couplings.
