PIRSA:13020148 Scientific Series Condensed Matter

DOI10.48660/13020148

Series: Quantum Matter

Ryu, S. (2013). Gravitational anomaly and topological phases. Perimeter Institute. https://pirsa.org/13020148

Ryu, Shinsei. Gravitational anomaly and topological phases. Perimeter Institute, Feb. 28, 2013, https://pirsa.org/13020148 

@misc{ pirsa_PIRSA:13020148,
  doi = {10.48660/13020148},
  url = {https://pirsa.org/13020148},
  author = {Ryu, Shinsei},
  keywords = {Condensed Matter},
  language = {en},
  title = {Gravitational anomaly and topological phases},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {feb},
  note = {PIRSA:13020148 see, \url{https://pirsa.org}}
}

Abstract

Since the quantum Hall effect, the notion of topological phases of matter has been extended to those that are well-defined (or: ``protected'') in the presence of a certain set of symmetries, and that exist in dimensions higher than two. In the (fractional) quantum Hall effects (and in ``chiral'' topological phases in general), Laughlin's thought experiment provides a key insight into their topological characterization; it shows a close connection between topological phases and quantum anomalies. By taking various examples, I will demonstrate that quantum anomalies serve as a useful tool to diagnose (and even define) topological properties of the systems. For chiral topological phases in (2+1) dimensions and (3+1) dimensional topological superconductors, I will discuss topological responses of the system which involve a cross correlation between thermal transport, angular momentum, and entropy. We also argue that gravitational anomaly is useful to study symmetry protected topological phases in (2+1) dimensions.

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