**3 – 5 January 2017**at The Chinese University of Hong Kong

### Advanced Study Institutes

# Topology in condensed matter and high energy physics

In 2016, the discovery of topological phases of quantum matter was awarded for Nobel Prize. Topological phases of quantum matter now becomes a very important and hot topic in both condensed matter and high energy physics. For example, the recent discovery of topological insulators and topological superconductors have led to a lot of collaborations between condensed matter theorists and high energy theorists to understand the essential physics behind them and their general classifications in interacting systems.

This seminar focuses on:
(a)How to characterize different topological phases?
(b)How to classify topological phases/quantum anomaly in a systematic way?
(c)How to design topological materials and devices for future industrial purpose?
The first two questions are the most fundamental questions in this field. How to completely characterize the topological phases has been a controversial topic for more than two decades. It seems that those featureless topological phases are quite non-local and that there is no local order parameter to characterize them, since fractional charge and fractional statistics cannot be detected through any local measurement. However, recent studies have shown that for systems described by local Hamiltonians, it might be possible to encode all those nonlocal properties in a local way, named “the entanglement pattern”. Different entanglement patterns will be generated by different local consistent algebraic rules. Quantum states with different classes of entanglement patterns cannot connect to each other without phase transitions. Mathematically, it seems that the so called tensor category theory is a relevant and powerful tool for us to understand the characterization and classifications of topological phases. Hence, exploring these concepts and related mathematics will lead to revolutionary impact on this field. On the other hand, topological phases will usually emerge in systems with strong local interactions. At a practical level, how to design topological materials and devices is another important and interesting question.
On the other hand, there are more and more evidences showing that the first two questions are also highly relevant for the understanding of global quantum anomaly and strong coupling physics in high energy theory. In addition, the underlying topological quantum field theories, e.g., Chern Simons theory also play very important roles in both condensed matter theory and high energy theory.
In fact, there are more than 10 condensed matter and theory high energy groups doing relevant research on topological physics. This workshop provides Hong Kong researchers the opportunity to enhance their knowledge on topological physics in both condensed matter theory and high energy theory.