Kim, Isaac H. (2011) Stability of topologically invariant order parameters at finite temperature. , Pasadena, CA. (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20120713140540112

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Abstract
Topological entanglement entropy is a topological invariant which can detect topological order of quantum manybody ground state. We assume an existence of such order parameter at finite temperature which is invariant under smooth deformation of the subsystems, and study its stability under hamiltonian perturbation. We apply this assumption to a Gibbs state of hamiltonian which satisfies so called `strong commuting' condition, which we shall define in the paper. Interesting models in this category include local hamiltonian models based on quantum error correcting code. We prove a stability of such topologically invariant order parameter against arbitrary perturbation which can be expressed as a sum of geometrically local boundednorm terms. The first order correction against such perturbation vanishes in the thermodynamic limit.
Item Type:  Report or Paper (Discussion Paper)  

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Additional Information:  This research was supported in part by NSF under Grant No. PHY0803371, by ARO Grant No. W911NF0910442, and DOE Grant No. DEFG0392ER40701. I thank Steve Flammia, Jeongwan Haah, and Spyridon Michalakis for helpful discussions.  
Group:  IQIM, Institute for Quantum Information and Matter  
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Record Number:  CaltechAUTHORS:20120713140540112  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20120713140540112  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  32435  
Collection:  CaltechAUTHORS  
Deposited By:  Tony Diaz  
Deposited On:  19 Jul 2012 21:31  
Last Modified:  26 Dec 2012 15:32 
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