SciPost Phys. 6, 041 (2019) ·
published 2 April 2019

· pdf
Based on several previous examples, we summarize explicitly the general
procedure to gauge models with subsystem symmetries, which are symmetries with
generators that have support within a submanifold of the system. The gauging
process can be applied to any local quantum model on a lattice that is
invariant under the subsystem symmetry. We focus primarily on simple 3D
paramagnetic states with planar symmetries. For these systems, the gauged
theory may exhibit foliated fracton order and we find that the species of
symmetry charges in the paramagnet directly determine the resulting foliated
fracton order. Moreover, we find that gauging linear subsystem symmetries in 2D
or 3D models results in a selfduality similar to gauging global symmetries in
1D.
SciPost Phys. 6, 015 (2019) ·
published 31 January 2019

· pdf
Fracton models exhibit a variety of exotic properties and lie beyond the
conventional framework of gapped topological order. In a previous work, we
generalized the notion of gapped phase to one of foliated fracton phase by
allowing the addition of layers of gapped twodimensional resources in the
adiabatic evolution between gapped threedimensional models. Moreover, we
showed that the Xcube model is a fixed point of one such phase. In this paper,
according to this definition, we look for universal properties of such phases
which remain invariant throughout the entire phase. We propose multipartite
entanglement quantities, generalizing the proposal of topological entanglement
entropy designed for conventional topological phases. We present arguments for
the universality of these quantities and show that they attain nonzero
constant value in nontrivial foliated fracton phases.