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arXiv · 1806.08633

Foliated fracton order in the checkerboard model

Wilbur Shirley·Kevin Slagle·Xie Chen
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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.

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Wilbur Shirley, Kevin Slagle, Xie Chen. 2018-06-22. Foliated fracton order in the checkerboard model. https://doi.org/10.1103/physrevb.99.115123

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