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We study unusual gapped topological phases where they admit $\mathbb{Z}_N$ fractional excitations in the same manner as topologically ordered phases, yet their ground state degeneracy depends on the local geometry of the system.
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Cited in the paper.
We regard the graph as 1D, since it consists of 1 1 - and 0 0 -simplices (which correspond to edges and vertices, respectively)
Cited in the paper.
Throughout this paper, we focus on excitations of the first two terms given in Hamiltonian (5). This is because the excitations of the rest terms are conjugate of the ones of the first two terms
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2021
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2022
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S. D. Pace and X.-G. Wen, “Position-dependent excitations and uv/ir mixing in the 𝕫 N {\mathbb{z}}_{N} rank-2 toric code and its low-energy effective field theory,” Phys. Rev. B
2022
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