Domain Walls: Machine-Learning and Nuclear Quantum Effects

With the development of matrix mechanics in 1925 by Heisenberg, Born and Jordan, the current year 2025 marks precisely the hundredth birthday of modern quantum mechanics, a breakthrough theoretical achievement that paved the way for the fundamental understanding of matter and without which the countless innovations that shape our modern day technologies would by unthinkable. It was only four years later that another giant in the field of physics, Paul Dirac, acknowledged that The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved. [`Quantum Mechanics of Many-Electron Systems`, Proceedings of the Royal Society (1929), A, 123, 714-733]. Nowadays, however, aided by digital computers, which are themselves a product of modern quantum solid state research, an arsenal of ingenious numerical simulation methods like density functional theory (DFT) allows to at least approximately solve the analytically intractable equations of quantum mechanics with great precision, thus opening the possibility to predict,study and optimize new materials for applications like solar cells, hydrogen or CO2 storage, catalytic reactions and drug design, just to name a few. In particular, in the present project we focus on the transient regions separating different (albeit symmetry-equivalent) spatial crystal bulk regions in insulating and wide- gap semiconducting crystals, for which the name domain walls (DWs) has been coined. Intriguingly, these DWs often exhibit electronic and magnetic properties that vastly differ from those of the bulk crystal. Also, in contrast to static crystal interfaces, they can be manipulated by applying external electric and magnetic fields, which may lead to the development of a completely new class of extremely flexible electronic devices. However, simulating DWs often calls for relatively large system sizes that result in huge computation costs and excessively long computation times. In addition, at low temperatures it is known that in certain materials nuclear quantum effects (NQEs), which are neglected in standard DFT calculations since they are notoriously difficult and expensive to calculate, must have a profound impact on the calculated DW properties. Qute recently, however, it has been recognized that machine-learning methods can be successfully employed to gain enormous efficiency increases in both standard DFT and NQE calculations. Employing such ML-aided simulations, the goal of the present project, which is to study the influence of NQFs on the physical properties of DWs in simulation, moves within the realm of possibility.