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Commuting Pauli Hamiltonians as maps between free modules

Haah, Jeongwan (2013) Commuting Pauli Hamiltonians as maps between free modules. Communications in Mathematical Physics, 324 (2). pp. 351-399. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20120522-115934410

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Abstract

We study unfrustrated spin Hamiltonians that consist of commuting tensor products of Pauli matrices. Assuming translation-invariance, a family of Hamiltonians that belong to the same phase of matter is described by a map between modules over the translation-group algebra, so homological methods are applicable. In any dimension every point-like charge appears as a vertex of a fractal operator, and can be isolated with energy barrier at most logarithmic in the separation distance. For a topologically ordered system in three dimensions, there must exist a point-like nontrivial charge. A connection between the ground state degeneracy and the number of points on an algebraic set is discussed. Tools to handle local Clifford unitary transformations are given.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1204.1063arXivDiscussion Paper
http://dx.doi.org/10.1007/s00220-013-1810-2DOIArticle
http://link.springer.com/article/10.1007%2Fs00220-013-1810-2PublisherArticle
Additional Information:© 2013 Springer-Verlag Berlin Heidelberg. Received: 25 April 2012; Accepted: 10 April 2013. Published online: 10 October 2013. The author would like to thank Sergey Bravyi, Lawrence Chung, Alexei Kitaev, John Preskill, Eric Rains, and Ari Turner for useful discussions. The author thanks Tom Graber for giving an intuitive explanation for Proposition 8.2. The author is supported in part by the Institute for Quantum Information and Matter, an NSF Physics Frontier Center, and the Korea Foundation for Advanced Studies.
Group:Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Korea Foundation for Advanced StudiesUNSPECIFIED
Record Number:CaltechAUTHORS:20120522-115934410
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120522-115934410
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31596
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:22 May 2012 20:08
Last Modified:12 Nov 2013 22:10

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