At sufficiently low temperatures, many-particle quantum systems can enter a wide variety of exotic phases, much beyond the usual gas-liquid-solid paradigm. Only recently has it been discovered that some of these phases are uniquely characterized by long-ranged entanglement. Moreover, entanglement plays an important role in the thermalization dynamics in closed quantum many-body systems and it can be used as a resource, e.g., for quantum metrology. However, as compared to few-body entanglement, the theoretical treatment of entanglement between many particles is qualitatively more difficult, and it is highly elusive for experimental measurements.
We are interested in identifying phases and phenomena that can only be understood by studying their entanglement content, and we develop theoretical frameworks for describing many-body entanglement. In view of experimental studies, we also investigate which entanglement measures can be used to characterize these phases and we design protocols for measuring entanglement in experimental setups.