Classification of Topological Defects in Abelian Topological States

TL;DR

This paper provides a comprehensive classification scheme for extrinsic topological defects in (2+1)D Abelian topological states, linking defects to boundary classifications and analyzing their quantum properties.

Contribution

It introduces a general classification of point-like and line-like extrinsic defects by relating them to boundary defects and Lagrangian subgroups in Abelian topological states.

Findings

Classified topologically distinct boundaries using Lagrangian subgroups.

Analyzed quantum dimensions and braiding statistics of defects.

Connected defect types to boundary domain walls in topological phases.

Abstract

In this paper we propose the most general classification of point-like and line-like extrinsic topological defects in (2+1)-dimensional Abelian topological states. We first map generic extrinsic defects to boundary defects, and then provide a classification of the latter. Based on this classification, the most generic point defects can be understood as domain walls between topologically distinct boundary regions. We show that topologically distinct boundaries can themselves be classified by certain maximal subgroups of mutually bosonic quasiparticles, called Lagrangian subgroups. We study the topological properties of the point defects, including their quantum dimension, localized zero modes, and projective braiding statistics.