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Fracton order is a new kind of quantum order characterized by topological excitations that exhibit remarkable mobility restrictions and a robust ground state degeneracy (GSD) which can increase exponentially with system size.
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The relation between toric code Kitaev 2003 and BF theory Blau and Thompson 1991 is reviewed in the appendix of Ref. Slagle and Kim 2017b
1991
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A. Y. Kitaev, Russian Mathematical Surveys 52
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R. Solovay (MSRI Conference on the Mathematics of Quantum Computation, Berkeley, CA, 2000)
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A. Kitaev, Annals of Physics 303
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Other examples of topological excitations include ordinary electrons and the charge and flux excitations of toric code Kitaev 2003
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S. Vijay, J. Haah, and L. Fu, Phys. Rev. B 92
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X.-G. Wen, National Science Review 3
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S. Vijay, J. Haah, and L. Fu, Phys. Rev. B 94
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H. Ma, E. Lake, X. Chen, and M. Hermele, Phys. Rev. B 95
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T. H. Hsieh and G. B. Halász, Phys. Rev. B 96
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G. B. Halász, T. H. Hsieh, and L. Balents, Phys. Rev. Lett. 119
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O. Petrova and N. Regnault, Phys. Rev. B 96
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W. Shirley, K. Slagle, Z. Wang, and X. Chen, arXiv:1712.05892 (2017)
2017
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B. Shi and Y.-M. Lu, arXiv:1705.09300 (2017)
2017
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B. J. Brown, D. Loss, J. K. Pachos, C. N. Self, and J. R. Wootton, Rev. Mod. Phys. 88
2016
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D. J. Williamson, Phys. Rev. B 94
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(a), In Vijay et al. 2016 , a Z N Z_{N} generalization of the X-cube model was given. However, their Z N Z_{N} model only generalizes to lattices with bipartite 3-cells. That is, the vertices of every 3-cell must form a bipartite lattice. In our figures, we present an alternative Z N Z_{N} generalization which does not require bipartite 3-cells. However, our generalization has a peculiarity where odd integer system sizes can result in a reduced GSD. For simplicity, we will focus on the Z 2 Z_{2} model in the main text, for which X † = X X^{\dagger}=X
2016
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S. Rastgoo and M. Requardt, Phys. Rev. D 94
2016
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A. Rasmussen, Y.-Z. You, and C. Xu, arXiv:1601.08235 (2016)
2016
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2017
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A. Prem, J. Haah, and R. Nandkishore, Phys. Rev. B 95
2017
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M. Pretko and L. Radzihovsky, arXiv:1711.11044 (2017)
2017
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H. He, Y. Zheng, B. A. Bernevig, and N. Regnault, arXiv:1710.04220 (2017)
2017
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(b), Ground state degeneracies were calculated using a method equivalent to the method described in Appendix B of Ref. Ma et al. 2017
2017
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Interestingly, in Ref. Shirley et al. 2017 it is shown that a local unitary transformation can connect H 2 H_{2} to the union of H 4 H_{4} and decoupled stacks of toric code
2017
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G. M. D’Ariano, International Journal of Theoretical Physics 56
2017
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T. Devakul, S. A. Parameswaran, and S. L. Sondhi, Phys. Rev. B 97
2018
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H. Ma, A. T. Schmitz, S. A. Parameswaran, M. Hermele, and R. M. Nandkishore, Phys. Rev. B 97
2018
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