  We study a stochastic lattice gas of particles in one dimension with strictly
finite-range interactions that respect the fracton-like conservation laws of
total charge and dipole moment. As the charge density is varied, the
connectivity of the system's charge configurations under the dynamics changes
qualitatively. We find two distinct phases: Near half filling the system
thermalizes subdiffusively, with almost all configurations belonging to a
single dynamically connected sector. As the charge density is tuned away from
half filling there is a phase transition to a frozen phase where locally active
finite bubbles cannot exchange particles and the system fails to thermalize.
The two phases exemplify what has recently been referred to as weak and strong
Hilbert space fragmentation, respectively. We study the static and dynamic
scaling properties of this weak-to-strong fragmentation phase transition in a
kinetically constrained classical Markov circuit model, obtaining some
conjectured exact critical exponents.
