# Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States

## TL;DR

This paper demonstrates the creation of non-Abelian topological defects called genons in lattice fractional quantum Hall systems, showing their potential for experimental realization and their impact on ground-state degeneracy.

## Contribution

It introduces a method to engineer higher genus systems with twist defects in lattice FQH states and confirms the existence of genons in realistic microscopic models.

## Key findings

- Localized midgap states form around defects.
- Ground-state degeneracy increases with the number of defects.
- Genons can be created using cold atom systems with artificial gauge fields.

## Abstract

We investigate extrinsic wormholelike twist defects that effectively increase the genus of space in lattice versions of multicomponent fractional quantum Hall systems. Although the original band structure is distorted by these defects, leading to localized midgap states, we find that a new lowest flat band representing a higher genus system can be engineered by tuning local single-particle potentials. Remarkably, once local many-body interactions in this new band are switched on, we identify various Abelian and non-Abelian fractional quantum Hall states, whose ground-state degeneracy increases with the number of defects, i.e, with the genus of space. This sensitivity of topological degeneracy to defects provides a "proof of concept" demonstration that genons, predicted by topological field theory as exotic non-Abelian defects tied to a varying topology of space, do exist in realistic microscopic models. Specifically, our results indicate that genons could be created in the laboratory by combining the physics of artificial gauge fields in cold atom systems with already existing holographic beam shaping methods for creating twist defects.