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arXiv · 2211.09168

Ground state degeneracy of the Ising cage-net model

Xiuqi Ma·Ananth Malladi·Zongyuan Wang·Zhenghan Wang·Xie Chen
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Abstract

The Ising cage-net model, first proposed in Phys. Rev. X 9, 021010 (2019), is a representative type I fracton model with nontrivial non-abelian features. In this paper, we calculate the ground state degeneracy of this model and find that, even though it follows a similar coupled layer structure as the X-cube model, the Ising cage-net model cannot be "foliated" in the same sense as X-cube as defined in Phys. Rev. X 8, 031051 (2018). A more generalized notion of "foliation'' is hence needed to understand the renormalization group transformation of the Ising cage-net model. The calculation is done using an operator algebra approach that we develop in this paper, and we demonstrate its validity through a series of examples.

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Xiuqi Ma, Ananth Malladi, Zongyuan Wang, Zhenghan Wang, Xie Chen. 2022-11-16. Ground state degeneracy of the Ising cage-net model. https://doi.org/10.1103/physrevb.107.085123

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