Foliated fracton order in the checkerboard model

TL;DR

This paper demonstrates that the checkerboard model exhibits foliated fracton order, introduces a renormalization group transformation using toric code bilayers, and shows its equivalence to two copies of the X-cube model.

Contribution

It introduces a renormalization group method for the checkerboard model and characterizes its foliated fracton phase as equivalent to two X-cube models.

Findings

Checkerboard model exhibits foliated fracton order.

The model can be transformed into two X-cube models.

A renormalization group transformation using toric code bilayers is developed.

Abstract

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.