Twisted Fracton Models in Three Dimensions

Understand

We study novel three-dimensional gapped quantum phases of matter which support quasiparticles with restricted mobility, including immobile "fracton" excitations.

• So far, most existing fracton models may be instructively viewed as generalized Abelian lattice gauge theories.
• Here, by analogy with Dijkgraaf-Witten topological gauge theories, we discover a natural generalization of fracton models, obtained by twisting the gauge symmetries.
• Introducing generalized gauge transformation operators carrying an extra phase factor depending on local configurations, we construct a plethora of exactly solvable three-dimensional models, which we dub "twisted fracton models." A key result of our approach is to demonstrate the existence of rich non-Abelian fracton phases of distinct varieties in a three-dimensional system with finite-range interactions.