Periodic Reporting for period 3 - FACT (Factorizing the wave function of large quantum systems)
Berichtszeitraum: 2022-09-01 bis 2024-02-29
One of the greatest challenges of condensed-matter physics is to predict the properties of large and complex quantum systems, such as nanocrystals or molecular aggregates, as well as solids with large unit cells or with strong correlations. 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 faster and less energy-consuming. For many purposes, especially in the IT sector, a thorough understanding on the level of the smallest constituents, i.e. the electrons and the nuclei, is indispensable. If one aims at a genuine first-principles description, this goal is yet largely unattainable with present-day computing facilities. In principle, one has to face the fundamental equation of quantum mechanics, the many-particle Schrödinger equation. 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. To deal with 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. Moreover, most of these methods work well for some systems and certain questions, and not so well for others. For example, finite-order many-body perturbation theory (MP2, MP4, etc.) works well for molecules, but cannot be applied to bulk metals.
The goal 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 (e.g. electrons and nuclei), one factor is a regular wavefunction, satisfying a standard Schrödinger equation, while the other factor is a conditional probability amplitude that satisfies a more complicated Schrödinger-like equation with a non-local, non-linear and non-Hermitian Hamiltonian. The above-mentioned standard techniques can then be employed for the subsystem-Schrödinger equations. In particular, different standard techniques can be applied to different subsystems. What makes the exact factorization distinct from other embedding schemes is the fact that the derivation of equations of motion for the subsystems is done without approximation. The same universal procedure can be applied to any interacting quantum system and to any subdivision of the system. This makes the exact factorization an extremely powerful and versatile tool. The objective of this action is to exploit the power of the method in various, particularly challenging situations such as solids with strong long-range correlations a well as molecular processes with strong non-adiabatic couplings.
The goal 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 (e.g. electrons and nuclei), one factor is a regular wavefunction, satisfying a standard Schrödinger equation, while the other factor is a conditional probability amplitude that satisfies a more complicated Schrödinger-like equation with a non-local, non-linear and non-Hermitian Hamiltonian. The above-mentioned standard techniques can then be employed for the subsystem-Schrödinger equations. In particular, different standard techniques can be applied to different subsystems. What makes the exact factorization distinct from other embedding schemes is the fact that the derivation of equations of motion for the subsystems is done without approximation. The same universal procedure can be applied to any interacting quantum system and to any subdivision of the system. This makes the exact factorization an extremely powerful and versatile tool. The objective of this action is to exploit the power of the method in various, particularly challenging situations such as solids with strong long-range correlations a well as molecular processes with strong non-adiabatic couplings.
During the first 30 months of this action, the method has been successfully applied to a diverse set of scenarios. Those include: (i) Non-adiabatic dynamics in laser-driven molecules; (ii) Non-adiabatic effects in periodic solids, especially in phonon-driven superconductors; (iii) Electron-nuclear coupling in molecular junctions; (iv) Long-range correlations in periodic solids.
Significant progress beyond the state-of-the-art has been published in 15 articles and presented at 18 International Conferences, Schools, Workshops and Seminar series. Results include the highly accurate calculation of the topological phase diagram of a strongly correlated solid. In this work, the exact factorization is applied to electrons only, leading to an embedding of strongly correlated electrons in an environment of weakly correlated ones. In contrast to previous embedding schemes, which are local in real space, the new scheme allows the description of truly long-range correlations in strongly correlated solids. In the laser-induced dynamics of molecules and solids we have identified a Lorentz-type N-body force that appears as consequence of the non-adiabatic interactions between electrons and nuclei. This Lorentz force turns out to be essential in the dynamics of the "electronic water wheel", a molecular junction where the electronic current triggers a rotational motion of the molecule sandwiched in the junction. For phonon-driven superconductors, the developed density functional theory of superconductivity has been established as the gold standard for calculating material-specific superconducting properties: Critical temperatures of phonon-driven superconductors are reliably predicted within a few percent of experiment, as shown in Fig 1, and complex scenarios like the competition of superconductivity with a charge-density wave have been accurately described as well, see Fig 2. In normal metals, the same density functional yields the phonon-induced renormalization (the "wiggle") of the band structure near the Fermi energy, see Fig 3.