Fracton X-Cube Model

Subdimensional mobility constraints on a cubic lattice
Click lattice sites to create/annihilate fracton excitations
1
2J
X-Cube fracton topological order hosts exotic quasi-particles with strictly restricted mobility.
Fractons: completely immobile isolated excitations — cannot move alone.
Lineons: bound pairs that move only along a single axis (1D mobility).
Planons: bound quadruplets that move only within a 2D plane.
The Hamiltonian H = −A∑vAv − B∑cBc enforces these constraints via vertex and cube operators with Z₂ gauge structure.