CMSA Quantum Matter in Mathematics and Physics: Hybrid Fracton Orders
Nathanan Tantivasadakarn - Harvard University
I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”. First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.
Based on 2102.09555 and 2106.03842