Abstract
The X-cube model, a prototypical gapped fracton model, was shown in Ref. [1] to have a foliation structure. That is, inside the 3+1 D model, there are hidden layers of 2+1 D gapped topological states. A screw dislocation in a 3+1 D 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+1 D 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.
Highlights
Fracton models [2,3,4,5,6,7,8] are characterized by the peculiar feature that some of their gapped point excitations are completely localized or are restricted to move only in a lower dimensional submanifold
As the 2D layers in this case host nonchiral topological order, are there extra topological degeneracies associated with the screw dislocation? this is what we find in this work
We find that when the boundary condition at the dislocation matches with that on the outer boundary, a screw dislocation can introduce extra ground state degeneracy (GSD) compared to a hole in the system
Summary
Fracton models [2,3,4,5,6,7,8] are characterized by the peculiar feature that some of their gapped point excitations are completely localized or are restricted to move only in a lower dimensional submanifold. It captures many important features of gapped type I fracton models, including a ground state degeneracy that grows exponentially with linear system size, the existence of fracton and other sub-dimensional fractional excitations, and subleading linear entanglement scaling [9,10,11] We will apply this procedure to a variety of other lattice structures, including ones with open boundary conditions, with holes and with screw dislocations. We proceed to describe the minimal structure approach to calculate the ground state degeneracy of the X-cube model with and without boundaries, discussing how the Wilson loops bind together in each case (Sec. 2).
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