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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.more » « less
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Based on several previous examples, we summarize explicitly thegeneral procedure to gauge models with subsystem symmetries, which aresymmetries with generators that have support within a sub-manifold ofthe system. The gauging process can be applied to any local quantummodel on a lattice that is invariant under the subsystem symmetry. Wefocus primarily on simple 3D paramagnetic states with planar symmetries.For these systems, the gauged theory may exhibit foliated fracton orderand we find that the species of symmetry charges in the paramagnetdirectly determine the resulting foliated fracton order. Moreover, wefind that gauging linear subsystem symmetries in 2D or 3D models resultsin a self-duality similar to gauging global symmetries in 1D.more » « less
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Fracton models exhibit a variety of exotic properties and lie beyondthe conventional framework of gapped topological order. In , wegeneralized the notion of gapped phase to one of foliatedfracton phase by allowing the addition of layers of gappedtwo-dimensional resources in the adiabatic evolution between gappedthree-dimensional models. Moreover, we showed that the X-cube model is afixed point of one such phase. In this paper, according to thisdefinition, we look for universal properties of such phases which remaininvariant throughout the entire phase. We propose multi-partiteentanglement quantities, generalizing the proposal of topologicalentanglement entropy designed for conventional topological phases. Wepresent arguments for the universality of these quantities and show thatthey attain non-zero constant value in non-trivial foliated fractonphases.more » « less
