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arXiv · 2010.16414

FCC, Checkerboards, Fractons, and QFT

Pranay Gorantla·Ho Tat Lam·Nathan Seiberg·Shu-Heng Shao
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Abstract

We consider XY-spin degrees of freedom on an FCC lattice, such that the system respects some subsystem global symmetry. We then gauge this global symmetry and study the corresponding $U(1)$ gauge theory on the FCC lattice. Surprisingly, this $U(1)$ gauge theory is dual to the original spin system. We also analyze a similar $\mathbb{Z}_N$ gauge theory on that lattice. All these systems are fractonic. The $U(1)$ theories are gapless and the $\mathbb{Z}_N$ theories are gapped. We analyze the continuum limits of all these systems and present free continuum Lagrangians for their low-energy physics. Our $\mathbb{Z}_2$ FCC gauge theory is the continuum limit of the well known checkerboard model of fractons. Our continuum analysis leads to a straightforward proof of the known fact that this theory is dual to two copies of the $\mathbb{Z}_2$ X-cube model. We find new models and new relations between known models. The $\mathbb{Z}_N$ FCC gauge theory can be realized by coupling three copies of an anisotropic model of lineons and planons to a certain exotic $\mathbb{Z}_2$ gauge theory. Also, although for $N=2$ this model is dual to two copies of the $\mathbb{Z}_2$ X-cube model, a similar statement is not true for higher $N$.

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Pranay Gorantla, Ho Tat Lam, Nathan Seiberg, Shu-Heng Shao. 2020-10-30. FCC, Checkerboards, Fractons, and QFT. https://doi.org/10.1103/physrevb.103.205116

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