Fractons from polarons

Fractons are a type of emergent quasiparticle that 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 background bosonic excitations. In such models, individual low-energy quasiparticles cannot move freely, while bound pairs have drastically increased mobility. 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, experimentally 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 exhibits perfect fracton behavior to all orders in perturbation theory. We suggest diagnostic signatures of fractonic behavior, opening a door to use already existing experimental tools to study their unusual physics, such as universal gravitation and restricted thermalization. As an example, gravitational attraction manifests as phase separation of holes in doped antiferromagnets. In studying these models, we identify simple effective one-dimensional microscopic Hamiltonians featuring perfect fractonic behavior, paving the way to future studies on fracton physics in lower dimensions, where a wealth of numerical and analytical tools already exist. In these Hamiltonians we identify pair-hopping interactions as the mechanism of dipole motion, and argue that this may provide a connection to topological edge states in boundary fractonic systems.