Beyond Topological Order: Quantum Field Theory of X-Cube Fracton Order and Robust Degeneracy from Geometry*

Topologically ordered quantum phases of matter are often characterized by their topological excitations and degeneracy. Recently however, exactly solvable 3D lattice models have been discovered for a new kind of phase beyond topological order in which the topological excitations exhibit remarkable mobility restrictions [1,2]. These phases can have so-called fracton topological excitations, which are immobile when isolated from other fractons. Additionally, in type I fracton orders, a pair of fractons can move along a 2D surface and so-called lineons can only move along straight lines. Unlike liquid topologically ordered phases which are only sensitive to topology (e.g. ground state degeneracy only depends on topology of spatial manifold), fracton orders are also sensitive to the geometry of the lattice and are thus beyond topological order.

In this talk, I will briefly review the X-cube model of fracton order. I will then explain our work [3] on how this model can be described by a field theory (which is analogous to a TQFT). I will also explain how spatial curvature of the lattice can induce a stable ground state degeneracy.

[1] Vijay, Haah, Fu 1505.02576
[2] Haah 1101.1962
[3] Slagle, Kim 1704.03870