Topological phases of matter and quantum anomalies
Topological phases in condensed matter physics are states of matter whose existence relies essentially on quantum mechanics and which do not have any analogue in classical physics. They are characterized by, among others, peculiar dissipationless electronic transport phenomena and their exotic excitations that may obey an unusual form of exchange statistics. These properties make topological phases of matter as promising candidates for future electronics with low energy cost and an ideal platform for stable, decoherence-free, quantum computers.
During his Center appointment, Professor Ryu and his research team will develop a theoretical understanding of topological phases of matter that can arise in the presence of and/or because of strong electron correlations, by using the concept of quantum anomalies. Quantum anomalies are exotic phenomena where symmetries of the system, which we naively expect are respected, are actually destroyed by quantum mechanical effects. These extremely quantum mechanical phenomena can occur typically in topological phases of matter, and in fact they are often allowed only within topological phases. Thus, quantum anomalies can be used as a useful diagnostic tool to detect topological phases both in theoretical studies and in experiments.
By developing new theoretical methods that allow Professor Ryu and his group to treat interaction effects in topological phases, he will look for new kinds of topological phases of matter and novel fundamental topological effects in condensed matter systems. In particular, he will develop a theoretical tool which can identify new topological phases which are fully interacting and whose topological properties are protected by non-local and/or antiunitary symmetries such as parity and time-reversal symmetry. He will also study anomalous commutation relations obeyed by electron position operators (the coordinate non-commutativity) that arise in three-dimensional topological insulators and suggest a peculiar uncertainty relation of electron coordinates. Their possible connection to collective dynamics of interacting topological insulators will be explored.