Foliated fracton order in the checkerboard model

Understand

In this work, we show that the checkerboard model exhibits the phenomenon of foliated fracton order.

• We introduce a renormalization group transformation for the model that utilizes toric code bilayers as an entanglement resource, and show how to extend the model to general three-dimensional manifolds.
• Furthermore, we use universal properties distilled from the structure of fractional excitations and ground-state entanglement to characterize the foliated fracton phase and find that it is the same as two copies of the X-cube model.
• Indeed, we demonstrate that the checkerboard model can be transformed into two copies of the X-cube model via an adiabatic deformation.