Ground state degeneracy of the Ising cage-net model

TL;DR

This paper calculates the ground state degeneracy of the non-abelian Ising cage-net fracton model, revealing its unique non-foliated structure and introducing a generalized foliation concept for understanding its renormalization.

Contribution

It introduces an operator algebra method to compute the ground state degeneracy and shows the Ising cage-net model's distinct non-foliated nature compared to similar models.

Findings

Ground state degeneracy calculated for the Ising cage-net model.

The model cannot be foliated as the X-cube model.

A generalized foliation concept is proposed for this model.

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.