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Commuting-projector Hamiltonians for chiral topological phases built from parafermions

Son, Jun Ho and Alicea, Jason (2018) Commuting-projector Hamiltonians for chiral topological phases built from parafermions. Physical Review B, 97 (24). Art. No. 245144. ISSN 2469-9950. http://resolver.caltech.edu/CaltechAUTHORS:20180626-130432855

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Abstract

We introduce a family of commuting-projector Hamiltonians whose degrees of freedom involve ℤ_3 parafermion zero modes residing in a parent fractional-quantum-Hall fluid. These commuting-projector models inherit nontrivial Hall conductance from the parent quantum-Hall states in which they are defined, and thus can describe chiral topological phases. The two simplest models in this family emerge from dressing Ising-paramagnet and toric-code spin models with parafermions; we study their edge properties, anyonic excitations, and ground-state degeneracy. We show that the first model realizes a symmetry-enriched topological phase (SET) for which ℤ_2 spin-flip symmetry from the Ising paramagnet permutes the anyons. Interestingly, the interface between this SET and the parent quantum-Hall phase realizes symmetry-enforced ℤ_3 parafermion criticality with no fine-tuning required. The second model exhibits a non-Abelian phase that is consistent with SU(2)_4 topological order, and can be accessed by gauging the ℤ_2 symmetry in the SET. Employing Levin-Wen string-net models with ℤ_2-graded structure, we generalize this picture to construct a large class of commuting-projector models for ℤ_2 SETs and non-Abelian topological orders exhibiting the same relation. Our construction provides the first commuting-projector-Hamiltonian realization of chiral bosonic non-Abelian topological order.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.97.245144DOIArticle
http://arxiv.org/abs/1803.11195arXivDiscussion Paper
Additional Information:© 2018 American Physical Society. (Received 6 April 2018; published 26 June 2018) We would like to thank D. Aasen, B. Bauer, M. Cheng, P. Fendley, L. Fidkowski, J. Haegeman, C.-M. Jian, N. Tarantino, Zitao Wang, and B. Ware for illuminating discussions. We gratefully acknowledge partial support from the National Science Foundation through Grant No. DMR-1723367 and the Army Research Office under Grant Award No. W911NF-17-1-0323. This research was also supported by the Caltech Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant No. GBMF1250, and the Walter Burke Institute for Theoretical Physics at Caltech.
Group:Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
NSFDMR-1723367
Army Research OfficeW911NF-17-1-0323
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationGBMF1250
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Record Number:CaltechAUTHORS:20180626-130432855
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180626-130432855
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87348
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:26 Jun 2018 20:17
Last Modified:26 Jun 2018 20:17

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