# Non-Abelian defects in Fracton phase of matter

## TL;DR

This paper explores non-Abelian defects in fracton phases of matter, revealing how twisted defects with non-Abelian zero modes can be engineered and used for fault-tolerant quantum computation.

## Contribution

It introduces a method to create and manipulate twisted defects with non-Abelian properties in abelian fracton models, expanding potential quantum computing applications.

## Key findings

- Twisted defects carry projective non-Abelian zero modes.
- Defects can be engineered via onsite hybridization along branch cuts.
- Braiding defects yields non-Abelian Berry phases for quantum computation.

## Abstract

Fracton phase of matter host fractionalized topological quasiparticles with restricted mobility. A wide variety of fracton models with abelian excitations had been proposed and extensively studied while the candidates for non-Abelian fracton phases are less explored. In this work, we investigate the effect of twisted defect in abelian fracton models. The twisted defect is launched by introducing a branch cut line hosting anyon condensate. In particular, these twisted defects, which alter different types of quasiparticles, carry projective non-Abelian zero modes. En route, such defects can be engineered via strong onsite hybridization along a branch cut which provides wide tunability and flexibility in experiment platforms. The braiding of twisted defects with projective non-Abelian Berry phase renders a new avenue toward fault-tolerant quantum computation.