Symmetry and Topology in Quantum Matter
Dr. Chang-Tse Hsieh (謝長澤博士)
Kavli Institute for the Physics and Mathematics of the Universe, Japan
Date 2020.03.05 (Thu)
Every physicist knows the importance of symmetry in physics. Symmetry in nature can be broken in (at least) three different ways: explicitly, spontaneously, and anomalously; understanding the latter two ways of symmetry breaking has been leading to significant developments in modern physics. For example, the Landau-Ginzburg-Wilson paradigm developed around mid-20th century guides the classification of conventional phases of condensed matter, such as magnets, crystals, and superfluids, based on types of spontaneous symmetry breaking (SSB). However, the discovery of quantum Hall effects in the ’80s and of topological insulators even more recently shows the existence of phases outside the framework of SSB, and it has been realized that the interplay between symmetry and topology is in general more subtle and a much richer phenomenology than previously thought can result. On the other hand, quantum anomalies—occurring when symmetries are broken by quantum effects—were initially studied in high energy physics, such as the chiral anomaly in the understanding of pion decays and the parity anomaly from a fundamental field-theory viewpoint, but they have recently been known to play an important role in condensed matter physics, as, for example, the above two kinds of anomalies can also emerge in Weyl semimetals and on the surface of topological insulators, respectively. In this seminar, I will talk about how symmetries can be understood and classified from a topological perspective, as well as applications of such a study to quantum condensed matter.