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Spin chains, defects, and quantum wires for the quantum-double edge

Albert, Victor V. and Aasen, David and Xu, Wenqing and Ji, Wenjie and Alicea, Jason and Preskill, John (2021) Spin chains, defects, and quantum wires for the quantum-double edge. . (Unpublished)

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Non-Abelian defects that bind Majorana or parafermion zero modes are prominent in several topological quantum computation schemes. Underpinning their established understanding is the quantum Ising spin chain, which can be recast as a fermionic model or viewed as a standalone effective theory for the surface-code edge -- both of which harbor non-Abelian defects. We generalize these notions by deriving an effective Ising-like spin chain describing the edge of quantum-double topological order. Relating Majorana and parafermion modes to anyonic strings, we introduce quantum-double generalizations of non-Abelian defects. We develop a way to embed finite-group valued qunits into those valued in continuous groups. Using this embedding, we provide a continuum description of the spin chain and recast its non-interacting part as a quantum wire via addition of a Wess-Zumino-Novikov-Witten term and non-Abelian bosonization.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Albert, Victor V.0000-0002-0335-9508
Aasen, David0000-0002-6552-488X
Alicea, Jason0000-0001-9979-3423
Preskill, John0000-0002-2421-4762
Additional Information:Attribution 4.0 International (CC BY 4.0). We thank Daniel Arovas, Maissam Barkeshli, Barry Bradlyn, Michele Burrello, Aaron Chew, Iris Cong, Jan von Delft, Paul Fendley, Hrant Gharibyan, Andrey Gromov, Jonathan Gross, Bailey Gu, Alexander Jahn, Alexei Kitaev, Peter Kopietz, Gleb Kotoousov, Ashley Milsted, Olexei Motrunich, Sepehr Nezami, Kevin Slagle, Lev Spodyneiko, Michael Stone, Eugene Tang, Cenke Xu, Oleg Yevtushenko, Yi-Zhuang You, and Erez Zohar for valuable discussions. We gratefully acknowledge support from the Walter Burke Institute for Theoretical Physics at Caltech. The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center. Contributions to this work by NIST, an agency of the US government, are not subject to US copyright. Any mention of commercial products does not indicate endorsement by NIST. V.V.A. thanks Olga Albert, Halina and Ryhor Kandratsenia, as well as Tatyana and Thomas Albert for providing daycare support throughout this work.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Record Number:CaltechAUTHORS:20220113-182244311
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112878
Deposited By: George Porter
Deposited On:13 Jan 2022 21:03
Last Modified:13 Jan 2022 21:03

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