Fracton behavior in frustrated kagome spin models

Fractons are topological quasiparticles characterized by a limited mobility. While there exists a variety of models displaying this behavior, typical fracton systems require rather complicated many-particle interactions. Here, we discuss fracton behavior in simple classical spin models on the kagome lattice with frustrated two-body interactions only. The spin degrees of freedom may either be defined as three-state Potts, XY, or Heisenberg spins. The observed isolated fractons as well as bound fracton pairs in the three-state Potts model, however, behave considerably different compared to conventional type-I and type-II fracton models. An interpretation in terms of type-I fracton behavior and the formulation of an effective symmetric tensor gauge theory is still possible when defining the system as a 2D cut of a 3D cubic lattice model. Our classical Monte-Carlo simulations indicate a crossover into a glassy phase at low temperatures. Considering XY spins, the system may host fractional vortex excitations whose real-space locations are closely correlated with those of fractons. Finally, in the case of Heisenberg spins, the energy barriers of fractons vanish such that they are no longer stable.