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Gapless Hamiltonians for the toric code using the PEPS formalism

Fernández-González, Carlos and Schuch, Norbert and Wolf, Michael M. and Cirac, J. Ignacio and Pérez-García, David (2011) Gapless Hamiltonians for the toric code using the PEPS formalism. . (Submitted)

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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 (PEPS), and can be applied to a large class of two-dimensional systems to obtain gapless "uncle Hamiltonians".

Item Type:Report or Paper (Discussion Paper)
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Additional Information:We specially thank Bruno Nachtergaele for useful comments and discussions. This work has been partially funded by the Spanish grants I-MATH, MTM2008-01366, S2009/ESP-1594 and QUITEMAD, the European project QUEVADIS, 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
Gordon and Betty Moore FoundationUNSPECIFIED
Caltech Center for the Physics of Information (CPI)UNSPECIFIED
Army Research Office (ARO)W911NF-09-1-0442
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:26 Dec 2012 15:31

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