Fracton topological order, generalized lattice gauge theory, and duality

Sagar Vijay, Jeongwan Haah, Liang Fu
2016 Physical review B  
We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, point-like topological excitations, and sub-extensive topological degeneracy. We demonstrate a duality between fracton topological order and interacting spin systems with symmetries along extensive, lower-dimensional subsystems, which may be used to systematically search for and characterize fracton topological phases. Commutative algebra and elementary
more » ... ebra and elementary algebraic geometry provide an effective mathematical toolset for our results. Our work paves the way for identifying possible material realizations of fracton topological phases.
doi:10.1103/physrevb.94.235157 fatcat:dcddcw5sfzhrhawxnni5odp6va