Abstract
Levin-Wen string-net models provide a construction of (2+1)D topologically ordered phases of matter with anyonic localized excitations described by the Drinfeld center of a unitary fusion category. Anyon condensation is a mechanism for phase transitions between (2+1)D topologically ordered phases. We construct an extension of Levin-Wen models in which tuning a parameter implements anyon condensation. We also describe the classification of anyons in Levin-Wen models via representation theory of the tube algebra, and use a variant of the tube algebra to classify low-energy localized excitations in the condensed phase.
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Acknowledgments
This project began as an undergraduate research project for Jessica Christian in Summer 2020 led by Peter Huston and David Green. It then evolved into a chapter of Peter Huston’s PhD thesis from 2022. The authors would like to thank Corey Jones for suggesting this project and for many important ideas. The authors would also like to thank Dave Aasen, Maissam Barkeshli, Jacob Bridgeman, Fiona Burnell, and Yuan-Ming Lu for helpful comments and discussions. All the authors were all supported by NSF grant DMS 1654159. David Green and David Penneys were additionally supported by NSF grant DMS 2154389.
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ArXiv ePrint: 2303.04711
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Christian, J., Green, D., Huston, P. et al. A lattice model for condensation in Levin-Wen systems. J. High Energ. Phys. 2023, 55 (2023). https://doi.org/10.1007/JHEP09(2023)055
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DOI: https://doi.org/10.1007/JHEP09(2023)055