… statistics be naturally defined for fractons, given their complete immobility as … fractons can
be exchanged and show that their self-statistics is a key part of the characterization of fracton …

… symmetry leads to a twisted fracton order, with a “lineon” (or excitation confined to move
only in one dimension) with an analogue of semionic self-statistics. We also show that a variant …

… While individual fracton excitations are immobile, a pair of fractons are mobile within a plane
and have bosonic self-statistics. In the X-cube fracton phase, there is a second type of point-…

… three-dimensional fracton order, by … fracton order with quasiparticle excitations that are
mobile only along a subset of one-dimensional lines, and display a form of fractional self-statistics…

… to diagnose topological or fracton phases on quantum hardware. … of other topological and
fracton phases of quantum matter, … VI, we explore how self-statistics can also be harnessed to …

… In a parallel development, the concept of foliated fracton order (… The purpose of this paper
is to fill the gaps in the fracton literature … A systematic investigation of fracton self-statistics in n-…

… with nontrivial self-statistics and mutual … fracton orders appear in two broad categories: Type
I orders, such as the X-cube fracton order [5], host both immobile quasiparticles (fractons) as …

… L contains only condensed quasiparticles with bosonic self statistics, or by fermionic quantum
wires when L contains at least one condensed quasiparticle with fermionic self statistics. …

… We emphasize that the notions of foliated fracton orders and foliated fracton phases are
distinct; this is explained in Section III, where we discuss different definitions of phases relevant …

… In a broader sense, fracton systems constitute exotic states of … [22], we conjectured that these
two self-dual fracton codes … owing to the interplay between fracton and spin-glass physics. …