Published December 26, 2012
| Published + Submitted + Supplemental Material
Journal Article
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Gapless Hamiltonians for the Toric Code Using the Projected Entangled Pair State Formalism
Chicago
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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, and can be applied to a large class of two-dimensional systems to obtain gapless "uncle Hamiltonians."
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.Attached Files
Published - PhysRevLett.109.260401.pdf
Submitted - 1111.5817v2.pdf
Supplemental Material - ToricCodePertSM.pdf
Files
PhysRevLett.109.260401.pdf
Additional details
- Alternative title
- Gapless Hamiltonians for the toric code using the PEPS formalism
- Eprint ID
- 32422
- Resolver ID
- CaltechAUTHORS:20120713-104140016
- Spanish Grants
- I-MATH
- Spanish Grants
- MTM2008-01366
- Spanish Grants
- S2009/ESP-1594
- QUITEMAD
- European Project QUEVADIS
- Alexander von Humboldt Foundation
- Gordon and Betty Moore Foundation
- NSF
- PHY-0803371
- Army Research Office (ARO)
- W911NF-09-1-0442
- Created
-
2012-07-19Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter