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.