FCC, Checkerboards, Fractons, and QFT

TL;DR

This paper explores the duality and continuum limits of gauge theories on FCC lattices with fractonic properties, revealing new models and relations, including connections to checkerboard and X-cube models.

Contribution

It introduces new dualities between FCC lattice gauge theories and known fracton models, and provides free continuum Lagrangians for their low-energy physics.

Findings

The $U(1)$ FCC gauge theory is dual to the original spin system.

The $ ext{Z}_2$ FCC gauge theory is the continuum limit of the checkerboard fracton model.

New relations between known fracton models and novel models are established.

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 $N$.