Abstract
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 sub-manifold 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 self-duality similar to gauging global symmetries in 1D.
Highlights
We describe explicitly a systematic procedure for gauging models with subsystem symmetries which can be applied to any local quantum model with such symmetry
The key question is: what is the relation between the ungauged order under subsystem symmetry and the gauged fracton order? To address this question, we study the mapping between ungauged and gauged phases and propose a way to interpret the correspondence
This is similar to the case of global symmetries in 1D, where paramagnets are mapped into symmetry breaking phases, and symmetry protected topological (SPT) phases can map into SPTs
Summary
Gauging is a powerful tool in the study of gapped quantum phases with global symmetry. In 2D and 3D, gauging linear subsystem symmetries (which act on 1D lines) maps paramagnetic (trivially symmetric) phases and symmetry breaking phases into one another, while subsystem symmetry protected topological (SPT) phases [6] may map into themselves This is similar to the case of global symmetries in 1D, where paramagnets are mapped into symmetry breaking phases, and SPT phases can map into SPTs. In 3D, gauging planar subsystem symmetries leads to foliated fracton order, as defined in Refs. By counting the species of symmetry charges in the ungauged model, we can make direct connection to the foliated fracton order after gauging It is natural that subsystem symmetry symmetric states gauge into foliated fracton models since the added layer gauges into a deconfined 2D gauge theory with gapped topological order.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
