# Nematic phases and the breaking of double symmetries

## Abstract

In this paper, we present a phase classification of (effectively) two-dimensional non-Abelian nematics, obtained using the Hopf symmetry breaking formalism. In this formalism, one exploits the underlying double symmetry which treats both ordinary and topological modes on equal footing, i.e., as representations of a single (non-Abelian) Hopf symmetry. The method introduced in the literature [F.A. Bais, B.J. Schroers, J.K. Slingerland, Broken quantum symmetry and confinement phases in planar physics, Phys. Rev. Lett. 89 (2002) 181601; F.A. Bais, B.J. Schroers, J.K. Slingerland, Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory, JHEP 05 (2003) 068.] and further developed in a paper published in parallel [F.A. Bais, C.J.M. Mathy, The breaking of quantum double symmetries by defect condensation, 2006, arXiv:cond-mat/0602115.] allows for a full classification of defect mediated as well as ordinary symmetry breaking patterns and a description of the resulting confinement and/or liberation phenomena. After a summary of the formalism, we determine the double symmetries for tetrahedral, octahedral, and icosahedral nematics and their representations. Subsequently the breaking patterns which follow from the formation of admissible defect condensates are analyzed systematically. This leads to a host of new (quantum and classical) nematic phases. Our result consists of a listing of condensates, withmore »

- Authors:

- Department of Physics, Princeton University, Jadwin Hall, Princeton, NJ 08544 (United States). E-mail: cmathy@princeton.edu
- Institute for Theoretical Physics, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands). E-mail: bais@science.uva.nl

- Publication Date:

- OSTI Identifier:
- 20976741

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 322; Journal Issue: 3; Other Information: DOI: 10.1016/j.aop.2006.06.005; PII: S0003-4916(06)00123-0; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; CLASSIFICATION; CONDENSATES; DEGREES OF FREEDOM; GAUGE INVARIANCE; LIQUID CRYSTALS; QUANTUM FLUIDS; SYMMETRY; SYMMETRY BREAKING; THREE-DIMENSIONAL CALCULATIONS; TOPOLOGY; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Mathy, C.J.M., and Bais, F.A..
```*Nematic phases and the breaking of double symmetries*. United States: N. p., 2007.
Web. doi:10.1016/j.aop.2006.06.005.

```
Mathy, C.J.M., & Bais, F.A..
```*Nematic phases and the breaking of double symmetries*. United States. doi:10.1016/j.aop.2006.06.005.

```
Mathy, C.J.M., and Bais, F.A.. Thu .
"Nematic phases and the breaking of double symmetries". United States.
doi:10.1016/j.aop.2006.06.005.
```

```
@article{osti_20976741,
```

title = {Nematic phases and the breaking of double symmetries},

author = {Mathy, C.J.M. and Bais, F.A.},

abstractNote = {In this paper, we present a phase classification of (effectively) two-dimensional non-Abelian nematics, obtained using the Hopf symmetry breaking formalism. In this formalism, one exploits the underlying double symmetry which treats both ordinary and topological modes on equal footing, i.e., as representations of a single (non-Abelian) Hopf symmetry. The method introduced in the literature [F.A. Bais, B.J. Schroers, J.K. Slingerland, Broken quantum symmetry and confinement phases in planar physics, Phys. Rev. Lett. 89 (2002) 181601; F.A. Bais, B.J. Schroers, J.K. Slingerland, Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory, JHEP 05 (2003) 068.] and further developed in a paper published in parallel [F.A. Bais, C.J.M. Mathy, The breaking of quantum double symmetries by defect condensation, 2006, arXiv:cond-mat/0602115.] allows for a full classification of defect mediated as well as ordinary symmetry breaking patterns and a description of the resulting confinement and/or liberation phenomena. After a summary of the formalism, we determine the double symmetries for tetrahedral, octahedral, and icosahedral nematics and their representations. Subsequently the breaking patterns which follow from the formation of admissible defect condensates are analyzed systematically. This leads to a host of new (quantum and classical) nematic phases. Our result consists of a listing of condensates, with the corresponding intermediate residual symmetry algebra T{sub r} and the symmetry algebra U characterizing the effective 'low energy' theory of surviving unconfined and liberated degrees of freedom in the broken phase. The results suggest that the formalism is applicable to a wide variety of two-dimensional quantum fluids, crystals and liquid crystals.},

doi = {10.1016/j.aop.2006.06.005},

journal = {Annals of Physics (New York)},

number = 3,

volume = 322,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}