PIRSA:10100045 Scientific Series Quantum Information

DOI10.48660/10100045

Series: Perimeter Institute Quantum Discussions

Koenig, R. (2010). Anyonic entanglement renormalization. Perimeter Institute. https://pirsa.org/10100045

Koenig, Robert. Anyonic entanglement renormalization. Perimeter Institute, Oct. 13, 2010, https://pirsa.org/10100045 

@misc{ pirsa_PIRSA:10100045,
  doi = {10.48660/10100045},
  url = {https://pirsa.org/10100045},
  author = {Koenig, Robert},
  keywords = {Quantum Information},
  language = {en},
  title = {Anyonic entanglement renormalization},
  publisher = {Perimeter Institute},
  year = {2010},
  month = {oct},
  note = {PIRSA:10100045 see, \url{https://pirsa.org}}
}

Abstract

We introduce a family of variational ansatz states for chains of anyons which optimally exploits the structure of the anyonic Hilbert space. This ansatz is the natural analog of the multi-scale entanglement renormalization ansatz for spin chains. In particular, it has the same interpretation as a coarse-graining procedure and is expected to accurately describe critical systems with algebraically decaying correlations. We numerically investigate the validity of this ansatz using the anyonic golden chain and its relatives as a testbed. This demonstrates the power of entanglement renormalization in a setting with non-abelian exchange statistics, extending previous work on qudits, bosons and fermions in two dimensions. This is joint work with Ersen Bilgin.

Resources

Next talk

Related Talks