Michalakis, Spyridon and Pytel, Justyna (2011) Stability of Frustration-Free Hamiltonians. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20120716-075826310
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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.
| Item Type: | Report or Paper (Discussion Paper) | ||||||||
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| Additional Information: | 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. | ||||||||
| Group: | IQIM, Institute for Quantum Information and Matter | ||||||||
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| Record Number: | CaltechAUTHORS:20120716-075826310 | ||||||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20120716-075826310 | ||||||||
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| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||
| ID Code: | 32447 | ||||||||
| Collection: | CaltechAUTHORS | ||||||||
| Deposited By: | Tony Diaz | ||||||||
| Deposited On: | 19 Jul 2012 21:18 | ||||||||
| Last Modified: | 26 Dec 2012 15:32 |
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