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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)

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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)
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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:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-09-1-0442
Department of Energy (DOE)DE-FG03-92-ER40701
Record Number:CaltechAUTHORS:20120713-140540112
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32435
Deposited By: Tony Diaz
Deposited On:19 Jul 2012 21:31
Last Modified:02 Jun 2023 00:08

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