Haah, Jeongwan (2012) Commuting Pauli Hamiltonians as maps between free modules. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20120522-115934410
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We study unfrustrated spin Hamiltonians that consist of commuting tensor products of Pauli matrices. Assuming translation-invariance, we observe that the Hamiltonian is described by a map between modules over the translation group algebra, so homological methods are applicable. We show universal properties of topologically ordered phases in low spatial dimensions. Particularly, we prove that in three dimensions there exists a point-like charge that can be isolated with energy barrier at most logarithmic in the separation distance. The isolation is due to a fractal operator. We also develop tools to compute the ground state degeneracy and to handle local unitary transformations.
|Item Type:||Report or Paper (Working Paper)|
|Additional Information:||Date: 24 April 2012. 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. The author would like to thank Sergey Bravyi, Lawrence Chung, Alexei Kitaev, John Preskill, Eric Rains, and Ari Turner for useful discussions.|
|Group:||Institute for Quantum Information and Matter, IQIM|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Joy Painter|
|Deposited On:||22 May 2012 20:08|
|Last Modified:||26 Dec 2012 15:14|
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