Anyonic entanglement renormalization
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 multiscale 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.
Additional Information
© 2010 The American Physical Society. Received 12 June 2010; revised manuscript received 21 August 2010; published 21 September 2010. The authors thank Simon Trebst and the anonymous referees for numerous useful suggestions. They also thank Robert Pfeifer, Guifré Vidal and Julien Vidal for comments, and Jens Eisert for bringing to their attention. R.K. acknowledges support by the Swiss National Science Foundation SNF under Grant No. PA00P2-126220. He also thanks Station Q for their hospitality and Lukas Fidkowski, John Preskill and Ben Reichardt for discussions. E.B. is supported by DOE under Grant No. DE-FG03-92-E40701 and NSF under Grant No. PHY-0803371Attached Files
Published - Koenig2010p11487Phys_Rev_B.pdf
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Koenig2010p11487Phys_Rev_B.pdf
Additional details
Identifiers
- Eprint ID
- 20372
- Resolver ID
- CaltechAUTHORS:20101011-111314003
Funding
- Swiss National Science Foundation (SNF)
- PA00P2-126220
- Department of Energy (DOE)
- DE-FG03-92-E40701
- NSF
- PHY-0803371
Dates
- Created
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2010-11-24Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field