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Models for Gapped Boundaries and Domain Walls

Kitaev, Alexei and Kong, Liang (2012) Models for Gapped Boundaries and Domain Walls. Communications in Mathematical Physics, 313 (2). pp. 351-373. ISSN 0010-3616. doi:10.1007/s00220-012-1500-5.

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We define a class of lattice models for two-dimensional topological phases with boundary such that both the bulk and the boundary excitations are gapped. The bulk part is constructed using a unitary tensor category C as in the Levin-Wen model, whereas the boundary is associated with amodule category over C.We also consider domainwalls (or defect lines) between different bulk phases.Adomainwall is transparent to bulk excitations if the corresponding unitary tensor categories are Morita equivalent. Defects of higher codimension will also be studied. In summary, we give a dictionary between physical ingredients of lattice models and tensor-categorical notions.

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Additional Information:© 2012 Springer-Verlag. 24 May 2011; Accepted: 18 January 2012; Published online: 7 June 2012. LK thanks Robert König for introducing the Levin-Wen model to him, and Xiao-Gang Wen for a valuable comment on the physical meaning of defects of codimension 3. We thank John Preskill, Hector Bombin, Anton Kapustin and Yong-ShiWu for many inspiring conversations. This work was supported in part by NSF under Grant No. PHY-0803371. AK is also supported by ARO under Grant No. W911NF-09-1-0442. LK is supported by the Gordon and Betty Moore Foundation through Caltech’s Center for the Physics of Information, and NSF under Grant No. PHY-0803371, the Basic Research Young Scholars Program and the Initiative Scientific Research Program of Tsinghua University, and NSFC under Grant No. 11071134.
Funding AgencyGrant Number
Army Research Office (ARO)W911NF-09-1-0442
Gordon and Betty Moore FoundationUNSPECIFIED
Caltech Center for the Physics of InformationUNSPECIFIED
Tsinghua University Basic Research Young Scholars ProgramUNSPECIFIED
Tsinghua University Initiative Scientific Research ProgramUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20120720-094651607
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32603
Deposited On:20 Jul 2012 20:04
Last Modified:09 Nov 2021 21:28

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