| Summary: | The X-cube model, a prototypical gapped fracton model, has been shown to have
a foliation structure. That is, inside the 3+1D model, there are hidden layers
of 2+1D gapped topological states. A screw dislocation in a 3+1D lattice can
often reveal nontrivial features associated with a layered structure. In this
paper, we study the X-cube model on lattices with screw dislocations. In
particular, we find that a screw dislocation results in a finite change in the
logarithm of the ground state degeneracy of the model. Part of the change can
be traced back to the effect of screw dislocations in a simple stack of 2+1D
topological states, hence corroborating the foliation structure in the model.
The other part of the change comes from the induced motion of fractons or
sub-dimensional excitations along the dislocation, a feature absent in the
stack of 2+1D layers.
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