#### Alladi Ramakrishnan Hall

#### *Fracton Fusion and Statistics*

#### Shriya Pai, University of Colorado at Boulder

**Abstract*: Quite generally, universal properties of quasiparticle*

excitations, such as fusion and statistics of anyons in two dimensions,

play a central role in characterizing quantum phases of matter. In

this talk, I will first offer a pedagogical introduction to fracton phases

of matter, following which I will briefly review the theory of fusion and

braiding of gapped excitations in phases with intrinsic topological order.

Following this, I will discuss a systematic framework to describe fusion

and statistical processes of the restricted mobility excitations in fracton

phases of matter, and illustrate this using an example. This is

non-trivial, precisely because such a framework must incorporate the

restricted mobility, an ingredient that is simply not present e.g. for

anyons in two dimensions. I will also show how these restricted mobility

excitations have fundamentally new kinds of statistical processes that

differ from more familiar braiding statistics.

Done