Quantum Phases of Matter

One of the most ambitious challenges in quantum physics is the classification of all possible phases of matter. That is, the establishment of a kind of “periodic table” indicating the different behavior that many-body quantum systems can have at zero temperature. Although the precise definition of “phases” still has to be clarified, an extraordinary progress has taken place during the last decade in this field. In particular, a successful classification has been achieved for free fermionic systems, as well as for one-dimensional (interacting) spin and fermionic chains. In higher spatial dimensions, partial progress has been reached involving a deep understanding of topological and symmetry protected phases of matter. This multidisciplinary field of research combines concepts coming from condensed matter physics, quantum field theory, and quantum information. Furthermore, recent progress with cold atomic physics is expected to open up new questions and lead to new methods to describe and classify strongly-correlated quantum phases of matter. Researchers at Harvard and MPG have made important theoretical contributions to this field, and led experimental research in the preparation and control of strongly-correlated states.