# Model of chiral spin liquids with Abelian and non-Abelian topological phases

## Abstract

In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, the Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.

- Authors:

- Paul Scherrer Inst. (PSI), Villigen (Switzerland). Condensed Matter Theory Group
- Boston Univ., MA (United States). Dept. of Physics
- Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Division

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; Swiss National Science Foundation (SNSF); Boston Univ., MA (United States)

- OSTI Identifier:
- 1425001

- Alternate Identifier(s):
- OSTI ID: 1413563; OSTI ID: 1425000

- Report Number(s):
- BNL-114836-2017-JAAM; BNL-114843-2017-JAAM

Journal ID: ISSN 2469-9950; PRBMDO

- Grant/Contract Number:
- SC0012704; 2000021 153648; FG02-06ER46316; AC02-98CH10886

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 22; Journal ID: ISSN 2469-9950

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Quantum spin liquid; topological phases of matter; bosonization; conformal field theory; Green's function methods; Gross-Neveu model; Non-Abelian models; spin lattice models

### Citation Formats

```
Chen, Jyong-Hao, Mudry, Christopher, Chamon, Claudio, and Tsvelik, A. M.
```*Model of chiral spin liquids with Abelian and non-Abelian topological phases*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevB.96.224420.

```
Chen, Jyong-Hao, Mudry, Christopher, Chamon, Claudio, & Tsvelik, A. M.
```*Model of chiral spin liquids with Abelian and non-Abelian topological phases*. United States. doi:10.1103/PhysRevB.96.224420.

```
Chen, Jyong-Hao, Mudry, Christopher, Chamon, Claudio, and Tsvelik, A. M. Fri .
"Model of chiral spin liquids with Abelian and non-Abelian topological phases". United States.
doi:10.1103/PhysRevB.96.224420.
```

```
@article{osti_1425001,
```

title = {Model of chiral spin liquids with Abelian and non-Abelian topological phases},

author = {Chen, Jyong-Hao and Mudry, Christopher and Chamon, Claudio and Tsvelik, A. M.},

abstractNote = {In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, the Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.},

doi = {10.1103/PhysRevB.96.224420},

journal = {Physical Review B},

number = 22,

volume = 96,

place = {United States},

year = {Fri Dec 15 00:00:00 EST 2017},

month = {Fri Dec 15 00:00:00 EST 2017}

}