Nematic phases and the breaking of double symmetries
Abstract
In this paper, we present a phase classification of (effectively) twodimensional nonAbelian 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 (nonAbelian) 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:condmat/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). Email: cmathy@princeton.edu
 Institute for Theoretical Physics, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands). Email: 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: S00034916(06)001230; 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; THREEDIMENSIONAL CALCULATIONS; TOPOLOGY; TWODIMENSIONAL 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) twodimensional nonAbelian 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 (nonAbelian) 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:condmat/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 twodimensional 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}
}

We investigate the stability of a quadratic bandcrossing point (QBCP) in 2D fermionic systems. At the noninteracting level, we show that a QBCP exists and is topologically stable for a Berry flux {+}2{pi}, if the point symmetry group has either fourfold or sixfold rotational symmetries. This putative topologically stable freefermion QBCP is marginally unstable to arbitrarily weak shortrange repulsive interactions. We consider both spinless and spin1/2 fermions. Four possible ordered states result: a quantum anomalous Hall phase, a quantum spin Hall phase, a nematic phase, and a nematicspinnematic phase.

Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
We investigate the stability of a quadratic bandcrossing point (QBCP) in 2D fermionic systems. At the noninteracting level, we show that a QBCP exists and is topologically stable for a Berry flux +2pi if the point symmetry group has either fourfold or sixfold rotational symmetries. This putative topologically stable freefermion QBCP is marginally unstable to arbitrarily weak shortrange repulsive interactions. We consider both spinless and spin1/2 fermions. Four possible ordered states result: a quantum anomalous Hall phase, a quantum spin Hall phase, a nematic phase, and a nematicspinnematic phase. 
The breaking of quantum double symmetries by defect condensation
In this paper, we study the phenomenon of Hopf or more specifically quantum double symmetry breaking. We devise a criterion for this type of symmetry breaking which is more general than the one originally proposed in F.A. Bais, B.J. Schroers, J.K. Slingerland [Broken quantum symmetry and confinement phases in planar physics, Phys. Rev. Lett. 89 (2002) 181601]; Hopf symmetry breaking and confinement in (2+1)dimensional gauge theory, JHEP 05 (2003) 068], and therefore extends the number of possible breaking patterns that can be described consistently. We start by recalling why the extended symmetry notion of quantum double algebras is an optimalmore » 
Ordered phases of rigid cores having semiflexible tails. II. Model for smecticA and reentrantnematic phases with hard repulsions
The general partition function of the preceding paper is applied to the special cases of smecticA and nematic liquid crystals and isotropic liquids in bulk phases. The relative stabilities of the isotropic, nematic, smecticA, and reentrantnematic phases are studied as a function of temperature, pressure, tail flexibility, and tail length. The following thermodynamic and molecular ordering properties are studied in these phases and at the phase transitions: smecticA order parameter, core and tail intermolecular orientational order parameters, tail intramolecular orientational order parameter, density, and entropy. The role of the semiflexible tails in stabilizing the smecticA and reentrantnematic phases is explicitlymore »