Long-range interacting quantum systems

Many-body quantum physics with long-range interactions of variable range and strength can be studied in experiments with Rydberg atom arrays, dipolar systems, trapped ions, and cold atoms in cavities. This review identifies common and universal features induced by the long-range interactions such as the extensive or nonextensive character of the total energy and features that deviate from the case of short-range interactions. A comparison with the corresponding results for classical systems is presented.