  Fractons are a type of emergent quasiparticle which cannot move freely in
isolation, but can easily move in bound pairs. Similar phenomenology is found
in boson-affected hopping models, encountered in the study of polaron systems
and hole-doped Ising antiferromagnets, in which motion of a particle requires
the creation or absorption of bosonic excitations. We show that boson-affected
hopping models can provide a natural realization of fractons, either
approximately or exactly, depending on the details of the system. We first
consider a generic one-dimensional boson-affected hopping model, in which we
show that single particles move only at sixth order in perturbation theory,
while motion of bound states occurs at second order, allowing for a broad
parameter regime exhibiting approximate fracton phenomenology. We explicitly
map the model onto a fracton Hamiltonian featuring conservation of dipole
moment via integrating out the mediating bosons. We then consider a special
type of boson-affected hopping models with mutual hard-core repulsion between
particles and bosons, accessible in hole-doped mixed-dimensional Ising
antiferromagnets, in which the hole motion is one dimensional in an otherwise
two-dimensional antiferromagnetic background. We show that this system, which
is within the current reach of ultracold-atom experiments, exhibits perfect
fracton behavior to all orders in perturbation theory, thereby enabling the
experimental study of dipole-conserving field theories. We further discuss
diagnostic signatures of fractonic behavior in these systems. In studying these
models, we also identify simple effective one-dimensional microscopic
Hamiltonians featuring perfect fractonic behavior, paving the way to future
studies on fracton physics in lower dimensions.
