  The discovery of fracton states of matter opens up an exciting, largely
unexplored field of many-body physics. Certain fracton states' similarity to
gravity is an intriguing property. In an earlier work [H. Yan, Phys. Rev. B 99,
155126 (2019)], we have demonstrated that a simple fracton model in anti-de
Sitter space satisfies several major holographic properties. In this follow-up
paper, we study the eight-vertex model dual to the original model. The dual
model has the advantage of illuminating the mutual information and subsystem
charges pictorially, which helps to reveal its connections to various other
topics in the study of holography and fracton phases. At zero temperature, the
dual eight-vertex model is a discrete realization of the bit-thread model, a
powerful tool developed to visualize holography. The bit-thread picture
combined with subsystem charges can give a quantitative account of the isometry
between the bulk and the boundary at finite energy, which is also a key issue
for holography. The black hole microscopic degrees of freedom can be identified
in this picture, which turn out to be encoded non-locally on the horizon. The
eight-vertex model proves to be a very helpful venue to improve our
understanding of the hyperbolic fracton model as a toy model of holography.
