Recently, exactly solvable 3D lattice models have been discovered for a new kind of phase, dubbed fracton topological order, in which the topological excitations are immobile or are bound to lines or surfaces. Unlike liquid topologically ordered phases (e.g. Z_2 gauge theory), which are only sensitive to topology (e.g. the ground state degeneracy only depends on the topology of spatial manifold), fracton orders are also sensitive to the geometry of the lattice. This geometry dependence allows for remarkably new physics which was forbidden in topologically invariant phases of matter.

In this talk, I will review the X-cube model of fracton order. I will then explain how geometry dependence allows for braiding of point-like particles in this 3D phase and how the X-cube model can be described by a quantum field theory that is analogous to a topological quantum field theory (TQFT). Incredibly, the gauge invariance of the field theory results in the mobility restrictions of the topological excitations by imposing a new kind of geometric charge conservation. [1]

I will explain how the X-cube model can be defined on more general lattices and spatial manifolds [2]. Remarkably, a lattice geometry with curvature can induce a robust ground state degeneracy even on a manifold with trivial topology. I will then discuss how lattice geometry affects the phase of matter in surprising ways. We will see that a previous definition of gapped phases of matter [3] may not be appropriate for fracton topological order, and I will introduce a new definition of phase of matter that is appropriate for phases with or without fractons. [4]

[1] Slagle, Kim 1708.04619

[2] Shirley, Slagle, Wang, Chen 1712.05892

[3] Chen, Gu, Wen 1004.3835

[4] Slagle, Kim 1712.04511

Coffee: 2:45 pm, 241 Compton