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Gapless Hamiltonians for the Toric Code Using the Projected Entangled Pair State Formalism

Fernández-González, Carlos and Schuch, Norbert and Wolf, Michael M. and Cirac, J. Ignacio and Pérez-García, David (2012) Gapless Hamiltonians for the Toric Code Using the Projected Entangled Pair State Formalism. Physical Review Letters, 109 (26). Art. No. 260401. ISSN 0031-9007.

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We study Hamiltonians which have Kitaev’s toric code as a ground state, and show how to construct a Hamiltonian which shares the ground space of the toric code, but which has gapless excitations with a continuous spectrum in the thermodynamic limit. Our construction is based on the framework of projected entangled pair states, and can be applied to a large class of two-dimensional systems to obtain gapless “uncle Hamiltonians.”

Item Type:Article
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URLURL TypeDescription Paper DOIArticle
Alternate Title:Gapless Hamiltonians for the toric code using the PEPS formalism
Additional Information:© 2012 American Physical Society. Received 20 June 2012; published 26 December 2012. We especially thank Bruno Nachtergaele for useful comments and discussions. This work has been partially funded by the Spanish Grants No. I-MATH, No. MTM2008- 01366, No. S2009/ESP-1594 and QUITEMAD, the European project QUEVADIS, the Alexander von Humboldt Foundation, the Gordon and Betty Moore Foundation through Caltech’s Center for the Physics of Information, the NSF Grant No. PHY-0803371, and the ARO Grant No. W911NF-09-1-0442. We also acknowledge the hospitality of the Centro de Ciencias de Benasque Pedro Pascual and of the Perimeter Institute, where part of this work was carried out.
Group:IQIM, Institute for Quantum Information and Matter
Funding AgencyGrant Number
Spanish GrantsI-MATH
Spanish GrantsMTM2008-01366
Spanish GrantsS2009/ESP-1594
Alexander von Humboldt FoundationUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Army Research Office (ARO)W911NF-09-1-0442
Classification Code:PACS numbers: 05.30.Rt, 03.65.Vf, 71.10.�w
Record Number:CaltechAUTHORS:20120713-104140016
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32422
Deposited By: Tony Diaz
Deposited On:19 Jul 2012 22:53
Last Modified:09 Jan 2016 01:00

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