Ground state degeneracy of the Ising cage-net model

• DOI: 10.48550/arxiv.2211.09168
• Publication Date: 2023-02-13
• Authors: Xiuqi Ma; Ananth Malladi; Zongyuan Wang; Zhenghan Wang; Xie Chen
• Keywords: Condensed Matter - Strongly Correlated Electrons; Strongly Correlated Electrons (cond-mat.str-el); 0103 physical sciences; FOS: Physical sciences; 530; 01 natural sciences

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.