Ising Fracton Spin Liquid on the Honeycomb Lattice

Fractons are quasiparticles which are incapable of independent motion. They arise naturally as a consequence of dipole conservation in higher-rank gauge theories. One route to experimental realization of fractonic physics is therefore to construct models realizing such exotic gauge theories, ideally built from short-ranged two-body interactions. This has been done successfully in the context of classical spin systems, however these models have been constructed from continuous degrees of freedom, making it impossible to isolate and study discrete fractons. Here, we present an Ising model exhibiting a fractonic spin liquid regime. We show explicitly that the excitations are fractons, appearing at the corners of membranes of spin flips. Because of the three-fold symmetry of the honeycomb lattice, these membranes can be locally combined such that no excitations are created, giving rise to a set of ground states described as a liquid of membranes. The liquid nature of the low-energy state sets our model apart from other known classical models that host fracton excitations. To study the finite-temperature behavior of the model, we devise a bespoke cluster Monte-Carlo algorithm, that moves pairs of defects and thus overcomes the freezing induced by the otherwise immobile excitations. We find evidence for a first order transition from a high-temperature paramagnet to a low-temperature phase whose correlations precisely match those predicted for a higher-rank Coulomb phase.