Numerical Evidence for a Haagerup Conformal Field Theory

Creators: Huang, Tzu-Chen; Lin, Ying-Hsuan; Ohmori, Kantaro; Tachikawa, Yuji; Tezuka, Masaki

Abstract

We numerically study an anyon chain based on the Haagerup fusion category and find evidence that it leads in the long-distance limit to a conformal field theory whose central charge is ∼2. Fusion categories generalize the concept of finite group symmetries to noninvertible symmetry operations, and the Haagerup fusion category is the simplest one which comes from neither finite groups nor affine Lie algebras. As such, ours is the first example of conformal field theories which have truly exotic generalized symmetries. Basically the same result was independently obtained in the preceding Letter [Phys. Rev. Lett. 128, 231602 (2022)].

Additional Information

© 2022 American Physical Society. Received 17 November 2021; revised 6 March 2022; accepted 18 April 2022; published 10 June 2022. The authors thank Minjae Cho, Yin-Chen He, Chang-Tse Hsieh, Yifan Wang, and Xi Yin for helpful discussions; Chang-Tse Hsieh, Justin Kaidi, Hosho Katsura, and Yunqin Zheng for comments on the draft; Masahiko G. Yamada for discussions on numerical algorithms; Matthew Fishman and Jie Ren for consultation through the ITensor Support Q&A; Gen Kuroki, Hosho Katsura, and Kensuke Tamura for help on setting up the Julia code; Paul Fendley, Alexander Hahn, Laurens Lootens, Tobias J. Osborne, Robijn Vanhove, Frank Verstraete, and Ramona Wolf for correspondences; and an anonymous referee for the discussions on finite-size scaling analysis. Finally, Y. T. thanks Yasuyuki Kawahigashi for first introducing him to the Haagerup subfactor a long time ago, which was the ultimate source of this project. The numerical computations were performed on the Harvard FAS Research Computing cluster and the IPMU iDark cluster. T. H. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Grant No. DE-SC0011632. Y. L. is supported by the Simons Collaboration Grant on the Non-Perturbative Bootstrap. Y. T. is partially supported by JSPS KAKENHI Grant-in-Aid (Wakate-A), No. 17H04837, and also by WPI Initiative, MEXT, Japan at IPMU, the University of Tokyo. M. T. is partially supported by JSPS KAKENHI No. JP17K17822, No. JP20K03787, No. JP20H05270, and No. JP21H05185.

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Published - PhysRevLett.128.231603.pdf

Submitted - 2110.03008.pdf

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