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Published October 15, 2014 | Submitted + Published
Journal Article Open

Stability of zero modes in parafermion chains

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.

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.

Attached Files

Published - PhysRevB.90.165106.pdf

Submitted - 1407.6376v3.pdf

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August 20, 2023
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October 18, 2023