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Topological Order in the Projected Entangled-Pair States Formalism: Transfer Operator and Boundary Hamiltonians

Schuch, Norbert and Poilblanc, Didier and Cirac, J. Ignacio and Pérez-García, David (2013) Topological Order in the Projected Entangled-Pair States Formalism: Transfer Operator and Boundary Hamiltonians. Physical Review Letters, 111 (9). Art. No. 090501. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20130924-112319746

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Abstract

We study the structure of topological phases and their boundaries in the projected entangled-pair states (PEPS) formalism. We show how topological order in a system can be identified from the structure of the PEPS transfer operator and subsequently use these findings to analyze the structure of the boundary Hamiltonian, acting on the bond variables, which reflects the entanglement properties of the system. We find that in a topological phase, the boundary Hamiltonian consists of two parts: A universal nonlocal part which encodes the nature of the topological phase and a nonuniversal part which is local and inherits the symmetries of the topological model, which helps to infer the structure of the boundary Hamiltonian and thus possibly of the physical edge modes.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1210.5601arXivDiscussion paper
http://dx.doi.org/10.1103/PhysRevLett.111.090501 DOIArticle
http://link.aps.org/doi/10.1103/PhysRevLett.111.090501PublisherArticle
Alternate Title:Topological order in PEPS: Transfer operator and boundary Hamiltonians
Additional Information:© 2013 American Physical Society. Received 28 October 2012; revised manuscript received 27 May 2013; published 27 August 2013. We acknowledge helpful discussions with F. Verstraete. N. S. acknowledges support by the Alexander von Humboldt Foundation, the Caltech Institute for Quantum Information and Matter (an NSF Physics Frontiers Center with the support of the Gordon and Betty Moore Foundation), and NSF Grant No. PHY-0803371. D. P. acknowledges support by the Agence Nationale de la Recherche under Grant No. ANR 2010 BLANC 0406-0 and CALMIP (Toulouse) for supercomputer resources. J. I. C. acknowledges support by the EU Project AQUTE, the DFG SFB 631 and Exzellenzcluster NIM, and Catalunya Caixa. D. P.-G. acknowledges QUEVADIS and Spanish Grants QUITEMAD and No. MTM2011-26912.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Alexander von Humboldt FoundationUNSPECIFIED
Caltech Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
NSFPHY-0803371
Agence Nationale de la RechercheANR 2010 BLANC 0406-0
EU Project AQUTEUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)SFB 631
Exzellenzcluster NIMUNSPECIFIED
Catalunya CaixaUNSPECIFIED
QUEVADISUNSPECIFIED
Spanish Grant QUITEMADUNSPECIFIED
Spanish GrantMTM2011-26912
Classification Code:PACS: 03.67.-a, 71.10.-w
Record Number:CaltechAUTHORS:20130924-112319746
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20130924-112319746
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:41502
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 Sep 2013 19:56
Last Modified:24 Sep 2013 19:56

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