# Topological insulating phases of non-Abelian anyonic chains

## Abstract

Boundary conformal field theory is brought to bear on the study of topological insulating phases of non- Abelian anyonic chains. These phases display protected anyonic end modes. We consider spin-1/2 su(2)t chains at any level k, focusing on the most prominent examples: the case k = 2 describes Ising anyons (equivalent to Majorana fermions) and k = 3 corresponds to Fibonacci anyons. The method we develop is quite general and rests on a deep connection between boundary conformal field theory and topological symmetry. This method tightly constrains the nature of the topological insulating phases of these chains for general k. Emergent anyons which arise at domain walls are shown to have the same braiding properties as the physical quasiparticles. This suggests a "solid-stat.e" topological quantum computation scheme in which emergent anyons are braided by tuning the couplings of non-Abelian quasiparticles in a fixed network.

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science - Office of Basic Energy Sciences - Materials Sciences and Engineering Division

- OSTI Identifier:
- 1393962

- DOE Contract Number:
- AC02-06CH11357

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 90; Journal Issue: 7

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
DeGottardi, Wade.
```*Topological insulating phases of non-Abelian anyonic chains*. United States: N. p., 2014.
Web. doi:10.1103/PhysRevB.90.075129.

```
DeGottardi, Wade.
```*Topological insulating phases of non-Abelian anyonic chains*. United States. doi:10.1103/PhysRevB.90.075129.

```
DeGottardi, Wade. Fri .
"Topological insulating phases of non-Abelian anyonic chains". United States.
doi:10.1103/PhysRevB.90.075129.
```

```
@article{osti_1393962,
```

title = {Topological insulating phases of non-Abelian anyonic chains},

author = {DeGottardi, Wade},

abstractNote = {Boundary conformal field theory is brought to bear on the study of topological insulating phases of non- Abelian anyonic chains. These phases display protected anyonic end modes. We consider spin-1/2 su(2)t chains at any level k, focusing on the most prominent examples: the case k = 2 describes Ising anyons (equivalent to Majorana fermions) and k = 3 corresponds to Fibonacci anyons. The method we develop is quite general and rests on a deep connection between boundary conformal field theory and topological symmetry. This method tightly constrains the nature of the topological insulating phases of these chains for general k. Emergent anyons which arise at domain walls are shown to have the same braiding properties as the physical quasiparticles. This suggests a "solid-stat.e" topological quantum computation scheme in which emergent anyons are braided by tuning the couplings of non-Abelian quasiparticles in a fixed network.},

doi = {10.1103/PhysRevB.90.075129},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

number = 7,

volume = 90,

place = {United States},

year = {Fri Aug 01 00:00:00 EDT 2014},

month = {Fri Aug 01 00:00:00 EDT 2014}

}