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Stability of topologically invariant order parameters at finite temperature

Kim, Isaac H. (2011) Stability of topologically invariant order parameters at finite temperature. , Pasadena, CA. (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20120713-140540112

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Abstract

Topological entanglement entropy is a topological invariant which can detect topological order of quantum many-body 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 bounded-norm terms. The first order correction against such perturbation vanishes in the thermodynamic limit.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1109.3496v1arXivUNSPECIFIED
Additional Information:This research was supported in part by NSF under Grant No. PHY-0803371, by ARO Grant No. W911NF-09-1-0442, and DOE Grant No. DE-FG03-92-ER40701. I thank Steve Flammia, Jeongwan Haah, and Spyridon Michalakis for helpful discussions.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
NSFPHY-0803371
Army Research Office (ARO)W911NF-09-1-0442
Department of Energy (DOE)DE-FG03-92-ER40701
Record Number:CaltechAUTHORS:20120713-140540112
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120713-140540112
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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