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Ising anyons in frustration-free Majorana-dimer models

Ware, Brayden and Son, Jun Ho and Cheng, Meng and Mishmash, Ryan V. and Alicea, Jason and Bauer, Bela (2016) Ising anyons in frustration-free Majorana-dimer models. Physical Review B, 94 (11). Art. No. 115127. ISSN 2469-9950. http://resolver.caltech.edu/CaltechAUTHORS:20160622-173202206

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Abstract

Dimer models have long been a fruitful playground for understanding topological physics. Here, we introduce a class, termed Majorana-dimer models, wherein bosonic dimers are decorated with pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian quasiparticles, and a topological p_x−ip_y superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We describe two parent Hamiltonians: one generalizes the well-known dimer model on the triangular lattice, while the other is most naturally understood as a model of decorated fluctuating loops on a honeycomb lattice. Using modular transformations, we show that the ground-state manifold of the latter model unambiguously exhibits all properties of the Ising×(p_x−ip_y) theory. We also discuss generalizations with more than one Majorana mode per site, which realize phases related to Kitaev's 16-fold way in a similar fashion.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevB.94.115127DOIArticle
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.94.115127PublisherArticle
http://arxiv.org/abs/1605.06125arXivDiscussion Paper
Additional Information:© 2016 American Physical Society. Received 15 June 2016; published 12 September 2016. We gratefully acknowledge C. Nayak for explaining the results in Refs. [14,15]; D. Aasen, X. Chen, Z.-C. Gu, R. Lutchyn, and H.-H. Tu for helpful discussions; and K. Walker for explaining his unpublished work. This work was supported by the NSF through Grant No. DMR-1341822 (J.A. and J.H.S.); the Caltech Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation; and the Walter Burke Institute for Theoretical Physics at Caltech.
Group:Institute for Quantum Information and Matter, IQIM, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
NSFDMR-1341822
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Record Number:CaltechAUTHORS:20160622-173202206
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160622-173202206
Official Citation:Ising anyons in frustration-free Majorana-dimer models Brayden Ware, Jun Ho Son, Meng Cheng, Ryan V. Mishmash, Jason Alicea, and Bela Bauer Phys. Rev. B 94, 115127
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68617
Collection:CaltechAUTHORS
Deposited By: Jacquelyn O'Sullivan
Deposited On:27 Jun 2016 16:27
Last Modified:12 Sep 2016 18:05

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