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Entropic topological invariant for a gapped one-dimensional system

Kim, Isaac H. (2014) Entropic topological invariant for a gapped one-dimensional system. Physical Review B, 89 (23). Art. No. 235120. ISSN 1098-0121. doi:10.1103/PhysRevB.89.235120.

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We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it is well defined even in the presence of arbitrary interaction and disorder. We also show that it is invariant under a finite-depth local quantum circuit, suggesting its stability against an arbitrary local perturbation that does not close the energy gap. Further, it can unambiguously distinguish a Majorana chain from a trivial chain under global fermion parity conservation. We argue that the order parameter can be, in principle, measured in an optical lattice system.

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Additional Information:© 2014 American Physical Society. Received 11 July 2013; revised manuscript received 6 June 2014; published 19 June 2014. I would like to thank Olivier Landon-Cardinal for clearing up the initial confusion I had in the subject. I would also like to thank John Preskill, AlexeiKitaev, Sankar Das Sarma, Jay Sau, Roger Mong, and Alexey Gorshkov for helpful discussions. 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.
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:23
Classification Code:PACS: 05.30.Rt, 03.65.Vf, 03.67.Mn, 71.10.Pm
Record Number:CaltechAUTHORS:20140911-104522486
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49587
Deposited By: Tony Diaz
Deposited On:11 Sep 2014 18:23
Last Modified:10 Nov 2021 18:46

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