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Anyonic entanglement renormalization

König, Robert and Bilgin, Ersen (2010) Anyonic entanglement renormalization. Physical Review B, 82 (12). Art. No. 125118. ISSN 0163-1829. https://resolver.caltech.edu/CaltechAUTHORS:20101011-111314003

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevB.82.125118DOIUNSPECIFIED
http://prb.aps.org/abstract/PRB/v82/i12/e125118PublisherUNSPECIFIED
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-0803371
Funders:
Funding AgencyGrant Number
Swiss National Science Foundation (SNF)PA00P2-126220
Department of Energy (DOE)DE-FG03-92-E40701
NSFPHY-0803371
Issue or Number:12
Classification Code:PACS: 03.65.Vf, 03.67.Lx, 05.10.Cc, 05.30.Pr
Record Number:CaltechAUTHORS:20101011-111314003
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20101011-111314003
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20372
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 Nov 2010 22:29
Last Modified:03 Oct 2019 02:09

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