Dual gauge field theory of quantum liquid crystals in three dimensions
Abstract
The dislocation-mediated quantum melting of solids into quantum liquid crystals is extended from two to three spatial dimensions, using a generalization of boson-vortex or Abelian-Higgs duality. Dislocations are now Burgers-vector-valued strings that trace out worldsheets in space-time while the phonons of the solid dualize into two-form (Kalb-Ramond) 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 emerge whenever translational symmetry is restored. Lastly, we also consider the effective electromagnetic response of electrically charged quantum liquid crystals, and find among other things that as a hard principle only two out of the possible three rotational Goldstone modes are observable using propagating electromagnetic fields.
- Authors:
-
- Keio Univ., Kanagawa (Japan)
- Leiden Univ., Leiden (The Netherlands); Aalto Univ., Aalto (Finland)
- SLAC National Accelerator Lab., Stanford Univ., Menlo Park, CA (United States)
- Leiden Univ., Leiden (The Netherlands)
- Publication Date:
- Research Org.:
- SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1408231
- Grant/Contract Number:
- AC02-76SF00515; S1511006; 694248
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 16; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 36 MATERIALS SCIENCE
Citation Formats
Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, and Zaanen, Jan. Dual gauge field theory of quantum liquid crystals in three dimensions. United States: N. p., 2017.
Web. doi:10.1103/physrevb.96.165115.
Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, & Zaanen, Jan. Dual gauge field theory of quantum liquid crystals in three dimensions. United States. https://doi.org/10.1103/physrevb.96.165115
Beekman, Aron J., Nissinen, Jaakko, Wu, Kai, and Zaanen, Jan. Mon .
"Dual gauge field theory of quantum liquid crystals in three dimensions". United States. https://doi.org/10.1103/physrevb.96.165115. https://www.osti.gov/servlets/purl/1408231.
@article{osti_1408231,
title = {Dual gauge field theory of quantum liquid crystals in three dimensions},
author = {Beekman, Aron J. and Nissinen, Jaakko and Wu, Kai and Zaanen, Jan},
abstractNote = {The dislocation-mediated quantum melting of solids into quantum liquid crystals is extended from two to three spatial dimensions, using a generalization of boson-vortex or Abelian-Higgs duality. Dislocations are now Burgers-vector-valued strings that trace out worldsheets in space-time while the phonons of the solid dualize into two-form (Kalb-Ramond) 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 emerge whenever translational symmetry is restored. Lastly, we also consider the effective electromagnetic response of electrically charged quantum liquid crystals, and find among other things that as a hard principle only two out of the possible three rotational Goldstone modes are observable using propagating electromagnetic fields.},
doi = {10.1103/physrevb.96.165115},
journal = {Physical Review. B},
number = 16,
volume = 96,
place = {United States},
year = {2017},
month = {10}
}
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Works referenced in this record:
Redundancies in Nambu-Goldstone Bosons
journal, May 2013
- Watanabe, Haruki; Murayama, Hitoshi
- Physical Review Letters, Vol. 110, Issue 18
Higgs mechanism for Kalb-Ramond gauge field
journal, November 1989
- Rey, Soo-Jong
- Physical Review D, Vol. 40, Issue 10
Nematic phases and the breaking of double symmetries
journal, March 2007
- Mathy, C. J. M.; Bais, F. A.
- Annals of Physics, Vol. 322, Issue 3
Stability analysis for -component Bose-Einstein condensate
journal, May 2006
- Roberts, David C.; Ueda, Masahito
- Physical Review A, Vol. 73, Issue 5
The topological theory of defects in ordered media
journal, July 1979
- Mermin, N. D.
- Reviews of Modern Physics, Vol. 51, Issue 3
Critical Properties of the N-Color London Model
journal, August 2004
- Smiseth, J.; Smørgrav, E.; Sudbø, A.
- Physical Review Letters, Vol. 93, Issue 7
Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models
journal, November 1966
- Mermin, N. D.; Wagner, H.
- Physical Review Letters, Vol. 17, Issue 22
Vortex Sublattice Melting in a Two-Component Superconductor
journal, March 2005
- Smørgrav, E.; Smiseth, J.; Babaev, E.
- Physical Review Letters, Vol. 94, Issue 9
Quantum and thermal melting of stripe forming systems with competing long-range interactions
journal, April 2017
- Mendoza-Coto, Alejandro; Barci, Daniel G.; Stariolo, Daniel A.
- Physical Review B, Vol. 95, Issue 14
Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x
journal, April 2016
- Hamidian, M. H.; Edkins, S. D.; Joo, Sang Hyun
- Nature, Vol. 532, Issue 7599
Vortex-Line Condensation in Three Dimensions: A Physical Mechanism for Bosonic Topological Insulators
journal, June 2015
- Ye, Peng; Gu, Zheng-Cheng
- Physical Review X, Vol. 5, Issue 2
Boson localization and the superfluid-insulator transition
journal, July 1989
- Fisher, Matthew P. A.; Weichman, Peter B.; Grinstein, G.
- Physical Review B, Vol. 40, Issue 1
Critical Fluctuations in Superconductors and the Magnetic Field Penetration Depth
journal, June 1996
- Herbut, Igor F.; Tešanović, Zlatko
- Physical Review Letters, Vol. 76, Issue 24
Rotational elasticity and couplings to linear elasticity
journal, November 2013
- Böhmer, Cg; Tamanini, N.
- Mathematics and Mechanics of Solids, Vol. 20, Issue 8
Stripe melting and quantum criticality in correlated metals
journal, September 2012
- Mross, David F.; Senthil, T.
- Physical Review B, Vol. 86, Issue 11
Electronic liquid-crystal phases of a doped Mott insulator
journal, June 1998
- Kivelson, S. A.; Fradkin, E.; Emery, V. J.
- Nature, Vol. 393, Issue 6685
Divergent Nematic Susceptibility in an Iron Arsenide Superconductor
journal, August 2012
- Chu, J. -H.; Kuo, H. -H.; Analytis, J. G.
- Science, Vol. 337, Issue 6095
Anomalous Scaling Dimensions and Stable Charged Fixed Point of Type-II Superconductors
journal, April 2000
- Hove, J.; Sudbø, A.
- Physical Review Letters, Vol. 84, Issue 15
Disclinations, dislocations, and continuous defects: A reappraisal
journal, January 2008
- Kleman, M.; Friedel, J.
- Reviews of Modern Physics, Vol. 80, Issue 1
Vortices in Multicomponent Bose–Einstein Condensates
journal, April 2005
- Kasamatsu, Kenichi; Tsubota, Makoto; Ueda, Masahito
- International Journal of Modern Physics B, Vol. 19, Issue 11
Possible quantum liquid crystal phases of helium monolayers
journal, November 2016
- Nakamura, S.; Matsui, K.; Matsui, T.
- Physical Review B, Vol. 94, Issue 18
Electrical Resistivity Anisotropy from Self-Organized One Dimensionality in High-Temperature Superconductors
journal, March 2002
- Ando, Yoichi; Segawa, Kouji; Komiya, Seiki
- Physical Review Letters, Vol. 88, Issue 13
Number of Nambu-Goldstone bosons and its relation to charge densities
journal, December 2011
- Watanabe, Haruki; Brauner, Tomáš
- Physical Review D, Vol. 84, Issue 12
Topological phase fluctuations, amplitude fluctuations, and criticality in extreme type-II superconductors
journal, December 1999
- Nguyen, A. K.; Sudbø, A.
- Physical Review B, Vol. 60, Issue 22
Observing the fluctuating stripes in high-T c superconductors
journal, December 2007
- Cvetkovic, V.; Nussinov, Z.; Mukhin, S.
- EPL (Europhysics Letters), Vol. 81, Issue 2
Long range order and metastability in two dimensional solids and superfluids. (Application of dislocation theory)
journal, June 1972
- Kosterlitz, J. M.; Thouless, D. J.
- Journal of Physics C: Solid State Physics, Vol. 5, Issue 11
Theory of Two-Dimensional Melting
journal, July 1978
- Halperin, B. I.; Nelson, David R.
- Physical Review Letters, Vol. 41, Issue 2
Probing the character of ultra-fast dislocations
journal, November 2015
- Ruestes, C. J.; Bringa, E. M.; Rudd, R. E.
- Scientific Reports, Vol. 5, Issue 1
Defect-mediated melting and the breaking of quantum double symmetries
journal, June 2006
- Bais, F. A.; Mathy, C. J. M.
- Physical Review B, Vol. 73, Issue 22
Electronic Liquid Crystal State in the High-Temperature Superconductor YBa2Cu3O6.45
journal, January 2008
- Hinkov, V.; Haug, D.; Fauque, B.
- Science, Vol. 319, Issue 5863
Generalized Liquid Crystals: Giant Fluctuations and the Vestigial Chiral Order of , , and Matter
journal, October 2016
- Liu, Ke; Nissinen, Jaakko; Slager, Robert-Jan
- Physical Review X, Vol. 6, Issue 4
Nematic Fermi Fluids in Condensed Matter Physics
journal, August 2010
- Fradkin, Eduardo; Kivelson, Steven A.; Lawler, Michael J.
- Annual Review of Condensed Matter Physics, Vol. 1, Issue 1
Classical direct interstring action
journal, April 1974
- Kalb, Michael; Ramond, P.
- Physical Review D, Vol. 9, Issue 8
Spontaneously Broken Spacetime Symmetries and Goldstone’s Theorem
journal, February 2002
- Low, Ian; Manohar, Aneesh V.
- Physical Review Letters, Vol. 88, Issue 10
Nematic Electronic Structure in the “Parent” State of the Iron-Based Superconductor Ca(Fe 1– x Co x ) 2 As 2
journal, January 2010
- Chuang, T. -M.; Allan, M. P.; Lee, Jinho
- Science, Vol. 327, Issue 5962
Non-commutative geometry and string field theory
journal, May 1986
- Witten, Edward
- Nuclear Physics B, Vol. 268, Issue 2
Spin- and Pair-Density-Wave Glasses
journal, July 2015
- Mross, David F.; Senthil, T.
- Physical Review X, Vol. 5, Issue 3
Electrodynamics of Abrikosov vortices: the field theoretical formulation
journal, September 2011
- Beekman, Aron J.; Zaanen, Jan
- Frontiers of Physics, Vol. 6, Issue 4
Duality in 2+1D quantum elasticity: superconductivity and quantum nematic order
journal, March 2004
- Zaanen, J.; Nussinov, Z.; Mukhin, S. I.
- Annals of Physics, Vol. 310, Issue 1
Type-II Bose-Mott insulators
journal, September 2012
- Beekman, Aron J.; Zaanen, Jan
- Physical Review B, Vol. 86, Issue 12
Melting and the vector Coulomb gas in two dimensions
journal, February 1979
- Young, A. P.
- Physical Review B, Vol. 19, Issue 4
Electron Nematic Phases Proliferate
journal, January 2010
- Fradkin, Eduardo; Kivelson, Steven A.
- Science, Vol. 327, Issue 5962
Existence of Long-Range Order in One and Two Dimensions
journal, June 1967
- Hohenberg, P. C.
- Physical Review, Vol. 158, Issue 2
Duality in field theory and statistical systems
journal, April 1980
- Savit, Robert
- Reviews of Modern Physics, Vol. 52, Issue 2
Broken spacetime symmetries and elastic variables
journal, July 2014
- Hayata, Tomoya; Hidaka, Yoshimasa
- Physics Letters B, Vol. 735
Quantum theory of a nematic Fermi fluid
journal, October 2001
- Oganesyan, Vadim; Kivelson, Steven A.; Fradkin, Eduardo
- Physical Review B, Vol. 64, Issue 19
Nematic world crystal model of gravity explaining absence of torsion in spacetime
journal, April 2004
- Kleinert, H.; Zaanen, J.
- Physics Letters A, Vol. 324, Issue 5-6
Classification of point-group-symmetric orientational ordering tensors
journal, August 2016
- Nissinen, Jaakko; Liu, Ke; Slager, Robert-Jan
- Physical Review E, Vol. 94, Issue 2
Hierarchy of orientational phases and axial anisotropies in the gauge theoretical description of generalized nematic liquid crystals
journal, February 2017
- Liu, Ke; Nissinen, Jaakko; de Boer, Josko
- Physical Review E, Vol. 95, Issue 2
An introduction to lattice gauge theory and spin systems
journal, October 1979
- Kogut, John B.
- Reviews of Modern Physics, Vol. 51, Issue 4
Role of nematic fluctuations in the thermal melting of pair-density-wave phases in two-dimensional superconductors
journal, March 2011
- Barci, Daniel G.; Fradkin, Eduardo
- Physical Review B, Vol. 83, Issue 10
Dual gauge field theory of quantum liquid crystals in two dimensions
journal, April 2017
- Beekman, Aron J.; Nissinen, Jaakko; Wu, Kai
- Physics Reports, Vol. 683
Theory of orientational elasticity
journal, February 1994
- Stallinga, S.; Vertogen, G.
- Physical Review E, Vol. 49, Issue 2
Spontaneous breaking of spacetime symmetries and the inverse Higgs effect
journal, April 2014
- Brauner, Tomáš; Watanabe, Haruki
- Physical Review D, Vol. 89, Issue 8
Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity
journal, November 2009
- Vojta, Matthias
- Advances in Physics, Vol. 58, Issue 6
Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
journal, June 2012
- Watanabe, Haruki; Murayama, Hitoshi
- Physical Review Letters, Vol. 108, Issue 25
Condensing Nielsen–Olesen strings and the vortex–boson duality in 3+1 and higher dimensions
journal, March 2011
- Beekman, A. J.; Sadri, D.; Zaanen, J.
- New Journal of Physics, Vol. 13, Issue 3
Ordering, metastability and phase transitions in two-dimensional systems
journal, April 1973
- Kosterlitz, J M; Thouless, D J
- Journal of Physics C: Solid State Physics, Vol. 6, Issue 7, p. 1181-1203
Vortex duality: Observing the dual nature using order propagators
journal, October 2006
- Cvetkovic, V.; Zaanen, J.
- Physical Review B, Vol. 74, Issue 13
Hausdorff Dimension of Critical Fluctuations in Abelian Gauge Theories
journal, September 2000
- Hove, J.; Mo, S.; Sudbø, A.
- Physical Review Letters, Vol. 85, Issue 11
Deconfining the rotational Goldstone mode: The superconducting quantum liquid crystal in (2+1) dimensions
journal, July 2013
- Beekman, Aron J.; Wu, Kai; Cvetkovic, Vladimir
- Physical Review B, Vol. 88, Issue 2
Quantum Smectic as a Dislocation Higgs Phase
journal, July 2006
- Cvetkovic, V.; Zaanen, J.
- Physical Review Letters, Vol. 97, Issue 4
What drives nematic order in iron-based superconductors?
journal, January 2014
- Fernandes, R. M.; Chubukov, A. V.; Schmalian, J.
- Nature Physics, Vol. 10, Issue 2
Dislocation-mediated melting of anisotropic layers
journal, January 1981
- Ostlund, S.; Halperin, B. I.
- Physical Review B, Vol. 23, Issue 1
Phase Transition in a Lattice Model of Superconductivity
journal, November 1981
- Dasgupta, C.; Halperin, B. I.
- Physical Review Letters, Vol. 47, Issue 21
Correspondence between two-dimensional bosons and a bulk superconductor in a magnetic field
journal, February 1989
- Fisher, Matthew P. A.; Lee, D. H.
- Physical Review B, Vol. 39, Issue 4
Field- and temperature-induced topological phase transitions in the three-dimensional -component London superconductor
journal, June 2005
- Smiseth, J.; Smørgrav, E.; Babaev, E.
- Physical Review B, Vol. 71, Issue 21
Anyon Superconductivity and Charge-Vortex Duality
journal, October 1991
- Lee, Dung-Hai; Fisher, Matthew P. A.
- International Journal of Modern Physics B, Vol. 05, Issue 16n17
Nonperturbative behavior of the quantum phase transition to a nematic Fermi fluid
journal, February 2006
- Lawler, Michael J.; Barci, Daniel G.; Fernández, Victoria
- Physical Review B, Vol. 73, Issue 8
Topological kinematic constraints: dislocations and the glide principle
journal, July 2006
- Cvetkovic, V.; Nussinov, Z.; Zaanen, J.
- Philosophical Magazine, Vol. 86, Issue 20
Dual Description of the Superconducting Phase Transition
journal, January 1995
- Kiometzis, Michael; Kleinert, Hagen; Schakel, Adriaan M. J.
- Fortschritte der Physik/Progress of Physics, Vol. 43, Issue 8
Charge-4e superconductivity from pair-density-wave order in certain high-temperature superconductors
journal, September 2009
- Berg, Erez; Fradkin, Eduardo; Kivelson, Steven A.
- Nature Physics, Vol. 5, Issue 11
The emergence of gauge invariance: The stay-at-home gauge versus local–global duality
journal, April 2012
- Zaanen, J.; Beekman, A. J.
- Annals of Physics, Vol. 327, Issue 4
Classification of nematic order in 2 + 1 dimensions: Dislocation melting and (2)/ lattice gauge theory
journal, February 2015
- Liu, Ke; Nissinen, Jaakko; Nussinov, Zohar
- Physical Review B, Vol. 91, Issue 7
Counting Rule for Nambu-Goldstone Modes in Nonrelativistic Systems
journal, February 2013
- Hidaka, Yoshimasa
- Physical Review Letters, Vol. 110, Issue 9
Nonrelativistic effective Lagrangians
journal, March 1994
- Leutwyler, H.
- Physical Review D, Vol. 49, Issue 6
Rotational Elasticity
journal, July 2011
- Bohmer, C. G.; Downes, R. J.; Vassiliev, D.
- The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 64, Issue 4
Origin of artificial electrodynamics in three-dimensional bosonic models
journal, March 2005
- Motrunich, O. I.; Senthil, T.
- Physical Review B, Vol. 71, Issue 12
Disclinations and first order transitions in 2D melting
journal, May 1983
- Kleinert, H.
- Physics Letters A, Vol. 95, Issue 7
Formation of a Nematic Fluid at High Fields in Sr3Ru2O7
journal, January 2007
- Borzi, R. A.; Grigera, S. A.; Farrell, J.
- Science, Vol. 315, Issue 5809
Vortex-boson duality in four space-time dimensions
journal, February 2007
- Franz, M.
- Europhysics Letters (EPL), Vol. 77, Issue 4
The Physics of Liquid Crystals
journal, May 1995
- de Gennes, P. G.; Prost, J.; Pelcovits, Robert
- Physics Today, Vol. 48, Issue 5
Multivalued Fields
conference, January 2007
- Kleinert, Hagen
- FRONTIERS OF FUNDAMENTAL PHYSICS: Eighth International Symposium FFP8, AIP Conference Proceedings
Liquid Crystals
journal, January 1977
- Gray, G. W.; Leadbetter, A. J.
- Physics Bulletin, Vol. 28, Issue 1
Theory of Two-Dimensional Melting.
journal, August 1978
- Halperin, B. I.; Nelson, David R.
- Physical Review Letters, Vol. 41, Issue 7
Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models
journal, December 1966
- Mermin, N. D.; Wagner, H.
- Physical Review Letters, Vol. 17, Issue 26
Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
text, January 2009
- Vojta, Matthias
- arXiv
Charge $4e$ superconductivity from pair density wave order in certain high temperature superconductors
text, January 2009
- Berg, E.; Fradkin, E.; Kivelson, S. A.
- arXiv
Condensing Nielsen-Olesen strings and the vortex-boson duality in 3+1 and higher dimensions
text, January 2010
- Beekman, A. J.; Sadri, D.; Zaanen, J.
- arXiv
The emergence of gauge invariance: the stay-at-home gauge versus local-global duality
text, January 2011
- Zaanen, J.; Beekman, A. J.
- arXiv
Counting rule for Nambu-Goldstone modes in nonrelativistic systems
text, January 2012
- Hidaka, Yoshimasa
- arXiv
Broken spacetime symmetries and elastic variables
text, January 2013
- Hayata, Tomoya; Hidaka, Yoshimasa
- arXiv
Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators
text, January 2014
- Ye, Peng; Gu, Zheng-Cheng
- arXiv
Detection of a Cooper-Pair Density Wave in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$
text, January 2015
- Hamidian, M. H.; Edkins, S. D.; Joo, Sang Hyun
- arXiv
Classification of point-group-symmetric orientational ordering tensors
text, January 2016
- Nissinen, Jaakko; Liu, Ke; Slager, Robert-Jan
- arXiv
Anomalous scaling dimensions and stable charged fixed-point of type-II superconductors
text, January 2000
- Hove, J.; Sudbo, A.
- arXiv
Hausdorff dimension of critical fluctuations in abelian gauge theories
text, January 2000
- Hove, J.; Mo, S.; Sudbo, A.
- arXiv
Critical properties of the N-color London model
text, January 2004
- Smiseth, J.; Smorgrav, E.; Sudbo, A.
- arXiv
Vortex sub-lattice melting in a two-component superconductor
text, January 2004
- Smorgrav, Eivind; Smiseth, Jo; Babaev, Egor
- arXiv
Field- and temperature induced topological phase transitions in the three-dimensional $N$-component London superconductor
text, January 2004
- Smiseth, J.; Smorgrav, E.; Babaev, E.
- arXiv
Vortices in multicomponent Bose-Einstein condensates
text, January 2005
- Kasamatsu, Kenichi; Tsubota, Makoto; Ueda, Masahito
- arXiv
Defect mediated melting and the breaking of quantum double symmetries
text, January 2006
- Bais, F. A.; Mathy, C. J. M.
- arXiv
Dual description of the superconducting phase transition
text, January 1995
- Kiometzis, M.; Kleinert, H.; Schakel, A. M. J.
- arXiv
Critical fluctuations in superconductors and the magnetic field penetration depth
text, January 1996
- Herbut, Igor F.; Tesanovic, Zlatko
- arXiv
Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem
text, January 2001
- Low, Ian; Manohar, Aneesh V.
- arXiv
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- Science, Vol. 358, Issue 6368
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