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Published December 26, 2012 | Version Published + Submitted + Supplemental Material
Journal Article Open

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

Creators

  • 1. ROR icon National University of Distance Education
  • 2. ROR icon Complutense University of Madrid
  • 3. ROR icon California Institute of Technology
  • 4. ROR icon RWTH Aachen University
  • 5. ROR icon Technical University of Munich
  • 6. ROR icon Max Planck Institute of Quantum Optics

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

1111.5817v2.pdf

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Additional details

Additional titles

Alternative title
Gapless Hamiltonians for the toric code using the PEPS formalism

Identifiers

Eprint ID
32422
Resolver ID
CaltechAUTHORS:20120713-104140016

Related works

Describes
http://arxiv.org/abs/1111.5817v2 (URL)

Funding

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

Dates

Created
2012-07-19
Created from EPrint's datestamp field
Updated
2021-11-09
Created from EPrint's last_modified field

Caltech Custom Metadata

Caltech groups
Institute for Quantum Information and Matter