Ground state degeneracy of the Ising cage-net model

Abstract

The Ising cage-net model, first proposed by Prem et al. [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 Shirley et al. [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.

Files

Additional details