Complex quantum systems which exhibit strong correlations are at the heart of many exciting phenomena and open problems in physics and beyond. For instance, in the fractional quantum Hall effect (FHQE), the electrons "fractionalize", i.e. break up into several parts, and this gives rise to novel robust ways to do ultra-precise measurements or to build a quantum computer. As another example, the study of complex molecules, such as for drug development, crucially relies on our ability to simulate complex correlated quantum systems. And fundamental questions about the constituents of matter, such as strong confinement of quarks, yet again have complex and strongly correlated quantum systems at their heart. Gaining a better understanding of these systems is thus important both from a fundamental and a technological point of view.
Yet, the same reason which makes these systems exhibit such a rich behavior also makes them extremely hard to understand: The presence of complex quantum correlations, termed "entanglement". Entanglement, on the other hand, has always been a central topic of study in Quantum Information Theory, where a wide range of tools for its understanding and manipulation has been developed. Thus, it is suggestive to apply quantum information concepts to enhance our understanding of complex quantum systems.
The goal of the project WASCOSYS - "Wavefunctions for strongly correlated systems" - has been to apply tools from Quantum Information Theory to build a framework for the study of complex quantum systems, based on their entanglement structure. The central tool are so-called tensor networks: They provide the natural language to describe those systems based on the structure of their entanglement, and allow to reconcile the local structure imposed by physical interactions with the globally emergent entanglement pattern which gives rise to exotic phases.
Throughout the project, our team has developed a diverse range of new tools to study and understand the physics of strongly correlated systems, and we have applied these tools to study a wide range of problems of interest in the field of unconventional quantum mechanical materials. Our results span a wide range from fundamental mathematical questions to realistic physical applications: We have established a systematic mathematical framework to fully classify all types of physics which exotic quantum materials can display, we have developed simulation techniques to provide an in-depth analysis of their properties, and we have applied all those to the wide range of physical materials where we expect to see unconventional physics driven by quantum effects. The results of the project will, in combination with experimental findings and quantum simulations, ultimately lead to new applications and materials based on strongly correlated quantum matter.
