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Stability of zero modes in parafermion chains

Jermyn, Adam S. and Mong, Roger S. K. and Alicea, Jason and Fendley, Paul (2014) Stability of zero modes in parafermion chains. Physical Review B, 90 (16). Art. No. 165106. ISSN 1098-0121. http://resolver.caltech.edu/CaltechAUTHORS:20141106-101230634

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Abstract

One-dimensional topological phases can host localized zero-energy modes that enable high-fidelity storage and manipulation of quantum information. Majorana fermion chains support a classic example of such a phase, having zero modes that guarantee twofold degeneracy in all eigenstates up to exponentially small finite-size corrections. Chains of “parafermions”—generalized Majorana fermions—also support localized zero modes, but, curiously, only under much more restricted circumstances. We shed light on the enigmatic zero-mode stability in parafermion chains by analytically and numerically studying the spectrum and developing an intuitive physical picture in terms of domain-wall dynamics. Specifically, we show that even if the system resides in a gapped topological phase with an exponentially accurate ground-state degeneracy, higher-energy states can exhibit a splitting that scales as a power law with system size, categorically ruling out exact localized zero modes. The transition to power-law behavior is described by critical behavior appearing exclusively within excited states.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1407.6376arXivArticle
http://dx.doi.org/10.1103/PhysRevB.90.165106 DOIArticle
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.165106PublisherArticle
Additional Information:© 2014 American Physical Society. Received 27 August 2014; revised manuscript received 23 September 2014; published 7 October 2014. We are indebted to David Clarke, Nate Lindner and Lesik Motrunich for illuminating conversations, as well as to Miles Stoudenmire for invaluable discussions on numerics. We also acknowledge funding from the NSF through grants DMR- 1341822 (A.J. and J.A.) and DMR/MPS1006549 (P.F.); the Alfred P. Sloan Foundation (J.A.); the Sherman Fairchild Foundation (R.M.); the Caltech Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation; the Caltech Summer Undergraduate Research Fellowship program along with partial support from the family of Jean J. Dixon (A.J.); and the Walter Burke Institute for Theoretical Physics at Caltech.
Group:IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
NSFDMR-1341822
NSFDMR/MPS1006549
Alfred P. Sloan FoundationUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Classification Code:PACS: 03.75.Lm, 03.65.Vf, 03.67.Bg, 03.67.Mn
Record Number:CaltechAUTHORS:20141106-101230634
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20141106-101230634
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51362
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Nov 2014 20:41
Last Modified:16 Dec 2014 18:19

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