Fracton Self-Statistics.

Fracton order describes novel quantum phases of matter that host quasiparticles with restricted mobility and, thus, lies beyond the existing paradigm of topological order. In particular, excitations that cannot move without creating multiple excitations are called fractons. Here, we address a fundamental open question-can the notion of self-exchange statistics be naturally defined for fractons, given their complete immobility as isolated excitations? Surprisingly, we demonstrate how fractons can be exchanged and show that their self-statistics is a key part of the characterization of fracton orders. We derive general constraints satisfied by the fracton self-statistics in a large class of Abelian fracton orders. Finally, we show the existence of nontrivial fracton self-statistics in some twisted variants of the checkerboard model and Haah's code, establishing that these models are in distinct quantum phases as compared to their untwisted cousins.