# Foliated fracton order in the Majorana checkerboard model

## TL;DR

This paper demonstrates that the Majorana checkerboard model exhibits foliated fracton order by establishing an entanglement renormalization scheme and an exact local unitary equivalence to the semionic X-cube model, revealing its phase structure.

## Contribution

It introduces an entanglement renormalization transformation and proves an exact local unitary equivalence, linking the Majorana checkerboard model to the X-cube phase.

## Key findings

- Majorana checkerboard model has foliated fracton order.
- The model is equivalent to the semionic X-cube model plus fermionic modes.
- Entanglement signatures confirm the fracton phase.

## Abstract

We establish the presence of foliated fracton order in the Majorana checkerboard model. In particular, we describe an entanglement renormalization group transformation which utilizes toric code layers as resources of entanglement, and furthermore discuss entanglement signatures and fractional excitations of the model. In fact, we give an exact local unitary equivalence between the Majorana checkerboard model and the semionic X-cube model augmented with decoupled fermionic modes. This mapping demonstrates that the model lies within the X-cube foliated fracton phase.