Published September 2013
| Version Submitted
Journal Article
Open
Stability of Frustration-Free Hamiltonians
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1.
California Institute of Technology
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2.
Nicolaus Copernicus University
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3.
Oregon State University
Abstract
We prove stability of the spectral gap for gapped, frustration-free Hamiltonians under general, quasi-local perturbations. We present a necessary and sufficient condition for stability, which we call Local Topological Quantum Order and show that this condition implies an area law for the entanglement entropy of the groundstate subspace. This result extends previous work by Bravyi et al. on the stability of topological quantum order for Hamiltonians composed of commuting projections with a common zero-energy subspace. We conclude with a list of open problems relevant to spectral gaps and topological quantum order.
Additional Information
© 2013 Springer-Verlag Berlin Heidelberg. Received: 19 September 2011; Accepted: 11 February 2013. Published online: 3 July 2013. Communicated by M. B. Ruskai. S. M. would like to thank Sergey Bravyi, Matt Hastings and Tobias Osborne for encouraging the pursuit of this result, Frank Verstraete for pointing out the connection of Local-TQO with the area-law for the entanglement entropy, Steve Flammia and Norbert Schuch for working out the details of that connection with the author, Robert Koenig and Bruno Nachtergaele for discussions on some of the technical details and Alexei Kitaev for several useful discussions on the extension of this result to general, gapped Hamiltonians. S.M. received support from NSF #DMS-0757581 and #PHY-0803371, and DOE Contract #DE-AC52-06NA25396. S. M. and J. P. are grateful for the warm hospitality of Los Alamos National Lab, where part of this work was completed during the summer of 2010, as well as to the referees whose thoughtful suggestions resulted in substantial improvement for both the clarity and the scope of this paper.Attached Files
Submitted - 1109.1588v2.pdf
Files
1109.1588v2.pdf
Additional details
Identifiers
- Eprint ID
- 32447
- DOI
- 10.1007/s00220-013-1762-6
- Resolver ID
- CaltechAUTHORS:20120716-075826310
Related works
- Describes
- 10.1007/s00220-013-1762-6 (DOI)
- http://arxiv.org/abs/1109.1588v2 (URL)
Funding
- NSF
- DMS-0757581
- NSF
- PHY-0803371
- Department of Energy (DOE)
- DE-AC52-06NA25396
Dates
- Created
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2012-07-19Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field
Caltech Custom Metadata
- Caltech groups
- Institute for Quantum Information and Matter