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) http://resolver.caltech.edu/CaltechAUTHORS:20120713-104140016
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Abstract
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 | ||||||||||||||||||||
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| Record Number: | CaltechAUTHORS:20120713-104140016 | ||||||||||||||||||||
| Persistent URL: | http://resolver.caltech.edu/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 | ||||||||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||||||||||
| Deposited On: | 19 Jul 2012 22:53 | ||||||||||||||||||||
| Last Modified: | 26 Dec 2012 15:31 |
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