Periodic Reporting for period 2 - SEQUAM (Symmetries and Entanglement in Quantum Matter)
Période du rapport: 2022-04-01 au 2023-09-30
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.
1. We have established a powerful framework which allows us to characterize the most general way in which symmetries in quantum materials can act on the entanglement, linking it to intricate mathematical structures, and broadly explored the ramifications of these different symmetry actions in the types of exotic quantum order which these systems can display. This forms a key step to a full classification of exotic quantum phases.
2. We have demonstrated that it is not always necessary to enforce exact symmetries, but that these symmetries can emerge in complex quantum materials; and we have established a set of tools to study and characterize such emergent symmetries. This significantly advances our understanding of symmetries in quantum materials, and our ability to characterize them.
3. We have established a range of tools to identify and characterize exotic entangled quantum phases and transitions between them in numerical simulations and beyond. These tools make use of the direct access to the entanglement degrees of freedom provided by tensor networks, and thus allow to go significantly beyond other probes.
4. We have developed a set of approaches to prepare exotic quantum states in realistic setups, and to investigate the exotic quantum order which they exhibit through practical probes, further advancing our ability to experimentally realize novel quantum materials.