Dual gauge field theory of quantum liquid crystals in two dimensions
Abstract
We present a selfcontained review of the theory of dislocationmediated quantum melting at zero temperature in two spatial dimensions. The theory describes the liquidcrystalline phases with spatial symmetries in between a quantum crystalline solid and an isotropic superfluid: quantum nematics and smectics. It is based on an AbelianHiggstype duality mapping of phonons onto gauge bosons (“stress photons”), which encode for the capacity of the crystal to propagate stresses. Dislocations and disclinations, the topological defects of the crystal, are sources for the gauge fields and the melting of the crystal can be understood as the proliferation (condensation) of these defects, giving rise to the Anderson–Higgs mechanism on the dual side. For the liquid crystal phases, the shear sector of the gauge bosons becomes massive signaling that shear rigidity is lost. After providing the necessary background knowledge, including the order parameter theory of twodimensional quantum liquid crystals and the dual theory of stress gauge bosons in bosonic crystals, the theory of melting is developed stepbystep via the disorder theory of dislocationmediated melting. Resting on symmetry principles, we derive the phenomenological imaginary time actions of quantum nematics and smectics and analyze the full spectrum of collective modes. The quantum nematic is a superfluidmore »
 Authors:
 Keio Univ., Kanagawa (Japan); National Institute for Materials Science, Ibaraki (Japan); RIKEN Center for Emergent Matter (CEMS), Saitama (Japan)
 Leiden Univ., Leiden (The Netherlands); Aalto Univ., Aalto (Finland)
 SLAC National Accelerator Lab. and Stanford Univ., Menlo Park, CA (United States)
 Leiden Univ., Leiden (The Netherlands)
 Washington Univ., St. Louis, MO (United States)
 Publication Date:
 Research Org.:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 OSTI Identifier:
 1368572
 Alternate Identifier(s):
 OSTI ID: 1373121
 Grant/Contract Number:
 AC0276SF00515; S1511006; DMR 1411229
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physics Reports
 Additional Journal Information:
 Journal Volume: 683; Journal Issue: C; Journal ID: ISSN 03701573
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 36 MATERIALS SCIENCE; quantum liquid crystals; quantum phase transitions; AbelianHiggs duality; superconductivity
Citation Formats
Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, Liu, Ke, Slager, Robert Jan, Nussinov, Zohar, Cvetkovic, Vladimir, and Zaanen, Jan. Dual gauge field theory of quantum liquid crystals in two dimensions. United States: N. p., 2017.
Web. doi:10.1016/j.physrep.2017.03.004.
Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, Liu, Ke, Slager, Robert Jan, Nussinov, Zohar, Cvetkovic, Vladimir, & Zaanen, Jan. Dual gauge field theory of quantum liquid crystals in two dimensions. United States. doi:10.1016/j.physrep.2017.03.004.
Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, Liu, Ke, Slager, Robert Jan, Nussinov, Zohar, Cvetkovic, Vladimir, and Zaanen, Jan. Tue .
"Dual gauge field theory of quantum liquid crystals in two dimensions". United States.
doi:10.1016/j.physrep.2017.03.004. https://www.osti.gov/servlets/purl/1368572.
@article{osti_1368572,
title = {Dual gauge field theory of quantum liquid crystals in two dimensions},
author = {Beekman, Aron J. and Nissinen, Jaakko and Wu, Kai and Liu, Ke and Slager, Robert Jan and Nussinov, Zohar and Cvetkovic, Vladimir and Zaanen, Jan},
abstractNote = {We present a selfcontained review of the theory of dislocationmediated quantum melting at zero temperature in two spatial dimensions. The theory describes the liquidcrystalline phases with spatial symmetries in between a quantum crystalline solid and an isotropic superfluid: quantum nematics and smectics. It is based on an AbelianHiggstype duality mapping of phonons onto gauge bosons (“stress photons”), which encode for the capacity of the crystal to propagate stresses. Dislocations and disclinations, the topological defects of the crystal, are sources for the gauge fields and the melting of the crystal can be understood as the proliferation (condensation) of these defects, giving rise to the Anderson–Higgs mechanism on the dual side. For the liquid crystal phases, the shear sector of the gauge bosons becomes massive signaling that shear rigidity is lost. After providing the necessary background knowledge, including the order parameter theory of twodimensional quantum liquid crystals and the dual theory of stress gauge bosons in bosonic crystals, the theory of melting is developed stepbystep via the disorder theory of dislocationmediated melting. Resting on symmetry principles, we derive the phenomenological imaginary time actions of quantum nematics and smectics and analyze the full spectrum of collective modes. The quantum nematic is a superfluid having a true rotational Goldstone mode due to rotational symmetry breaking, and the origin of this ‘deconfined’ mode is traced back to the crystalline phase. The twodimensional quantum smectic turns out to be a dizzyingly anisotropic phase with the collective modes interpolating between the solid and nematic in a nontrivial way. We also consider electrically charged bosonic crystals and liquid crystals, and carefully analyze the electromagnetic response of the quantum liquid crystal phases. In particular, the quantum nematic is a real superconductor and shows the Meissner effect. Furthermore, their special properties inherited from spatial symmetry breaking show up mostly at finite momentum, and should be accessible by momentumsensitive spectroscopy.},
doi = {10.1016/j.physrep.2017.03.004},
journal = {Physics Reports},
number = C,
volume = 683,
place = {United States},
year = {Tue Apr 18 00:00:00 EDT 2017},
month = {Tue Apr 18 00:00:00 EDT 2017}
}
Web of Science

We present a selfcontained review of the theory of dislocationmediated quantum melting at zero temperature in two spatial dimensions. The theory describes the liquidcrystalline phases with spatial symmetries in between a quantum crystalline solid and an isotropic superfluid: quantum nematics and smectics. It is based on an AbelianHiggstype duality mapping of phonons onto gauge bosons ("stress photons"), which encode for the capacity of the crystal to propagate stresses. Dislocations and disclinations, the topological defects of the crystal, are sources for the gauge fields and the melting of the crystal can be understood as the proliferation (condensation) of these defects, givingmore »Cited by 3

Dual gauge field theory of quantum liquid crystals in three dimensions
The dislocationmediated quantum melting of solids into quantum liquid crystals is extended from two to three spatial dimensions, using a generalization of bosonvortex or AbelianHiggs duality. Dislocations are now Burgersvectorvalued strings that trace out worldsheets in spacetime while the phonons of the solid dualize into twoform (KalbRamond) gauge fields. We propose an effective dual Higgs potential that allows for restoring translational symmetry in either one, two, or three directions, leading to the quantum analogues of columnar, smectic, or nematic liquid crystals. In these phases, transverse phonons turn into gapped, propagating modes, while compressional stress remains massless. Rotational Goldstone modes emergemore »Cited by 1 
Factorized Smatrices in two dimensions as the exact solutions of certain relativistic quantum field theory models
The general properties of the factorized Smatrix in twodimensional spacetime are considered. The relation between the factorization property of the scattering theory and the infinite number of conservation laws of the underlying field theory is discussed. The factorization of the total Smatrix is shown to impose hard restrictions on twoparticle matrix elements: they should satisfy special identities, the socalled factorization equations. The general solution of the unitarity, crossing and factorization equations is found for the Smatrices having isotopic O (N) symmetry. The solution turns out to have different properties for the cases N=2 and N> or =3. For N=2 themore » 
Nonlocal (parafermion) currents in twodimensional conformal quantum field theory and selfdual critical points in Z/sub N/symmetric statistical systems
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