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Perturbative analysis of topological entanglement entropy from conditional independence

Kim, Isaac H. (2012) Perturbative analysis of topological entanglement entropy from conditional independence. Physical Review B, 86 (24). Art. No. 245116. ISSN 1098-0121. doi:10.1103/PhysRevB.86.245116.

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We use the structure of conditionally independent states to analyze the stability of topological entanglement entropy. For the ground state of the quantum double or Levin-Wen model, we obtain a bound on the first-order perturbation of topological entanglement entropy in terms of its energy gap and subsystem size. The bound decreases superpolynomially with the size of the subsystem, provided the energy gap is nonzero. We also study the finite-temperature stability of stabilizer models, for which we prove a stronger statement than the strong subadditivity of entropy. Using this statement and assuming (i) finite correlation length and (ii) small conditional mutual information of certain configurations, first-order perturbation effect for arbitrary local perturbation can be bounded. We discuss the technical obstacles in generalizing these results.

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Additional Information:© 2012 American Physical Society. Received 9 February 2012; revised manuscript received 9 October 2012; published 18 December 2012. 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. The author would like to thank S. Michalakis, S. Flammia, J. Haah, S. Boixo, and A. Hamma for helpful discussions. The author would also like to thank the anonymous referees for their helpful suggestions in revising the paper.
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
Issue or Number:24
Classification Code:PACS: 03.65.Vf, 03.67.Pp
Record Number:CaltechAUTHORS:20130110-080914647
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36286
Deposited By: Tony Diaz
Deposited On:11 Jan 2013 22:04
Last Modified:09 Nov 2021 23:21

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