A central topic in physics is the study of different phases of matter, that is, the different ways in which complex systems can organize, and the resulting behavior they exhibit. Familiar examples are, e.g. water vs. ice, or magnetic vs. non-magnetic behavior of metals. The key to understanding these different behaviors are symmetries: By studying the symmetries of the physical laws which describe a given system and the way in which the system orders relative to those symmetries, we can classify the different phases of matter and characterize the way in which transitions between them happen. E.g. ice - unlike water - breaks the translational symmetry of the underlying physical laws, and magnetic materials break rotational symmetry.
This understanding has been challenged by the discovery of novel exotic phases - "quantum matter" - which organize in ways which cannot be understood in terms of symmetry breaking. Rather, the system displays non-trivial ordering in its complex global quantum correlations - quantum entanglement. These systems hold great potential for novel applications, such as measurement devices with unprecented precision, or as building blocks for powerful quantum computers. Given their technological importance, a full understanding of the different quantum materials and the physics they can exhibit, in analogy to the theory of symmetry breaking, is all the more pressing, as it would allow us to explore the entire range of future quantum materials, and use their full potential.
The goal of the project SEQUAM - "Symmetries and entanglement in quantum matter" - is to establish a systematic and comprehensive framework which allows to reconcile the notion of local symmetries and ordering relative to them with the global entanglement ordering displayed by quantum materials. A central tool is the formalism of tensor networks, which form a highly versatile language for the description of complex quantum systems, highlighting the role played by entanglement, but are also very successfully applied in other fields such as data science or artificial intelligence. Tensor networks provide us with direct access to the entanglement degrees of freedom in a local fashion, and are thus ideally suited to reconcile local symmetries and global entanglement. The resulting framework will provide us with the necessary tools to understand the different types of exotic order which quantum materials can exhibit, as well as with tools to probe this behavior in simulations and experiments, and enable us to identify novel useful applications of such exotic quantum materials. We will apply this framework to a wide range of systems which appear in condensed matter and high energy physics, or are realizable in quantum simulators, e.g. with cold gases.
The results of the project SEQUAM will give a unified understanding of unconventional phases, based on physical symmetries and the resulting entanglement order. It will yield their physical manifestations, numerical probes for their detection, and simple ways to realize and probe these models in experimental scenarios, and thus significantly advance our ability to understand, study, and realize complex quantum phases.
