We propose that the fracton models with subsystem symmetry can be a class of
toy models for the holographic principle. The discovery of the anti-de
Sitter/conformal field theory correspondence as a concrete construction of
holography and the subsequent developments including the subregion duality and
Ryu-Takayanagi formula of entanglement entropy have revolutionized our
understanding of quantum gravity and provided powerful tool sets for solving
various strongly-coupled quantum field theory problems. To resolve many
mysteries of holography, toy models can be very helpful. One example is the
holographic tensor networks which illuminate the quantum error correcting
properties of gravity in the anti-de Sitter space. In this work we discuss a
classical toy model featuring subsystem symmetries and immobile fracton
excitations. We show that such a model defined on the hyperbolic lattice
satisfies some key properties of the holographic correspondence. The correct
subregion duality and Ryu-Takayanagi formula for mutual information are
established for a connected boundary region. A naively defined black hole's
entropy scales as its horizon area. We also present discussions on corrections
for more complicated boundary subregions, the possible generalizations of the
model, and a comparison with the holographic tensor networks.Comment: 16 pages, 16 figures. Updated to the published version, with new
title, two new sections, and a lot revision
