Built on

T. J. Osborne, D. E. Stiegemann, and R. Wolf, (2019), arXiv:1906.01322 [math.CT]
Original
1906
Earlier work this paper cites.
L. Tagliacozzo, T. R. de Oliveira, S. Iblisdir, and J. I. Latorre, Phys. Rev. B 78
Original
1976
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R. J. Baxter, Journal of Physics A: Mathematical and General 13
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J. L. Cardy, Nucl. Phys. B 270
1986
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E. Witten, Phil. Trans. Roy. Soc. Lond. A 329
1989
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G. W. Moore and N. Seiberg, Commun. Math. Phys. 123
1989
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V. V. Bazhanov and N. Y. Reshetikhin, Int. J. Mod. Phys. A 4
1989
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G. Moore and N. Seiberg, in Physics, Geometry and Topology , NATO ASI Series, edited by H. C. Lee (Springer US, 1990) pp. 263–361
1990
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J. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge University Press, 1996)
1996
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P. Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory , 1st ed., Graduate Texts in Contemporary Physics (Springer-Verlag, 1997)
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V. Jones and V. S. Sunder, Introduction to Subfactors (Cambridge University Press, 1997)
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M. Asaeda and U. Haagerup, Comm. Math. Phys. 202
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J. Fuchs, I. Runkel, and C. Schweigert, Nucl. Phys. B 646
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J. Belletête, A. M. Gainutdinov, J. L. Jacobsen, H. Saleur, and T. S. Tavares, (2020), arXiv:2003.11293 [math-ph]
Original
2003
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A. Hahn and R. Wolf, Phys. Rev. B 102
Original
2004
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2021

A critical lattice model for a Haagerup conformal field theory

Vanhove, Robijn, Lootens, Laurens, Van Damme, Maarten et al.

Understand

We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions with the \emph{Haagerup fusion category} $\mathcal{H}_3$ as input data.

We present compelling numerical evidence in the form of finite entanglement scaling to support a Haagerup conformal field theory (CFT) with central charge $c=2$.
Generalized twisted CFT spectra are numerically obtained through exact diagonalization of the transfer matrix and the conformal towers are separated in the spectra through their identification with the topological sectors.
It is further argued that our model can be obtained through an orbifold procedure from a larger lattice model with input $Z(\mathcal{H}_3)$, which is the simplest modular tensor category that does not admit an algebraic construction.

Built on

T. J. Osborne, D. E. Stiegemann, and R. Wolf, (2019), arXiv:1906.01322 [math.CT]
Original
1906
Earlier work this paper cites.
L. Tagliacozzo, T. R. de Oliveira, S. Iblisdir, and J. I. Latorre, Phys. Rev. B 78
Original
1976
Earlier work this paper cites.
R. J. Baxter, Journal of Physics A: Mathematical and General 13
1980
Earlier work this paper cites.
J. L. Cardy, Nucl. Phys. B 270
1986
Earlier work this paper cites.
E. Witten, Phil. Trans. Roy. Soc. Lond. A 329
1989
Earlier work this paper cites.
G. W. Moore and N. Seiberg, Commun. Math. Phys. 123
1989
Earlier work this paper cites.
V. V. Bazhanov and N. Y. Reshetikhin, Int. J. Mod. Phys. A 4
1989
Earlier work this paper cites.
G. Moore and N. Seiberg, in Physics, Geometry and Topology , NATO ASI Series, edited by H. C. Lee (Springer US, 1990) pp. 263–361
1990
Earlier work this paper cites.
J. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge University Press, 1996)
1996
Earlier work this paper cites.
P. Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory , 1st ed., Graduate Texts in Contemporary Physics (Springer-Verlag, 1997)
1997
Earlier work this paper cites.
V. Jones and V. S. Sunder, Introduction to Subfactors (Cambridge University Press, 1997)
1997
Earlier work this paper cites.
M. Asaeda and U. Haagerup, Comm. Math. Phys. 202
1999
Earlier work this paper cites.
G. Felder, J. Frohlich, J. Fuchs, and C. Schweigert, Phys. Rev. Lett. 84
2000
Earlier work this paper cites.
M. Izumi, Rev. Math. Phys. 13
2001
Earlier work this paper cites.
V. B. Petkova and J. B. Zuber, Phys. Lett. B 504
2001
Earlier work this paper cites.
J. Fuchs, I. Runkel, and C. Schweigert, Nucl. Phys. B 646
2002
Earlier work this paper cites.
J. Belletête, A. M. Gainutdinov, J. L. Jacobsen, H. Saleur, and T. S. Tavares, (2020), arXiv:2003.11293 [math-ph]
Original
2003
Earlier work this paper cites.
A. Hahn and R. Wolf, Phys. Rev. B 102
Original
2004
Earlier work this paper cites.

Similar

J. Frohlich, J. Fuchs, I. Runkel, and C. Schweigert, Phys. Rev. Lett. 93
2004
Cited alongside, same era.
M. A. Levin and X.-G. Wen, Phys. Rev. B 71
2005
Cited alongside, same era.
P. Calabrese and J. L. Cardy, Int. J. Quant. Inf. 4
2006
Cited alongside, same era.
A. Feiguin, S. Trebst, A. W. W. Ludwig, M. Troyer, A. Kitaev, Z. Wang, and M. H. Freedman, Phys. Rev. Lett. 98
2007
Cited alongside, same era.
T.-C. Huang and Y.-H. Lin, (2020), arXiv:2007.00670 [math.CT]
Original
2007
Cited alongside, same era.
D. Aasen, P. Fendley, and R. S. K. Mong, (2020), arXiv:2008.08598 [cond-mat.stat-mech]
Original